network analysis research

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

• View all journals
• Explore content
• About the journal
• Publish with us
• Sign up for alerts
• Published: 19 August 2021

Network analysis of multivariate data in psychological science

• Denny Borsboom   ORCID: orcid.org/0000-0001-9720-4162 1 ,
• Marie K. Deserno 2 ,
• Mijke Rhemtulla 3 ,
• Sacha Epskamp 1 , 4 ,
• Eiko I. Fried 5 ,
• Richard J. McNally 6 ,
• Donald J. Robinaugh 7 ,
• Marco Perugini   ORCID: orcid.org/0000-0002-4864-6623 8 ,
• Jonas Dalege 9 ,
• Giulio Costantini 8 ,
• Adela-Maria Isvoranu   ORCID: orcid.org/0000-0001-7981-9198 1 ,
• Anna C. Wysocki 3 ,
• Claudia D. van Borkulo 1 , 4 ,
• Riet van Bork   ORCID: orcid.org/0000-0002-4772-8862 10 &
• Lourens J. Waldorp 1  

Nature Reviews Methods Primers volume  1 , Article number:  58 ( 2021 ) Cite this article

86k Accesses

421 Citations

398 Altmetric

Metrics details

• Scientific data

An Author Correction to this article was published on 21 February 2022

This article has been updated

In recent years, network analysis has been applied to identify and analyse patterns of statistical association in multivariate psychological data. In these approaches, network nodes represent variables in a data set, and edges represent pairwise conditional associations between variables in the data, while conditioning on the remaining variables. This Primer provides an anatomy of these techniques, describes the current state of the art and discusses open problems. We identify relevant data structures in which network analysis may be applied: cross-sectional data, repeated measures and intensive longitudinal data. We then discuss the estimation of network structures in each of these cases, as well as assessment techniques to evaluate network robustness and replicability. Successful applications of the technique in different research areas are highlighted. Finally, we discuss limitations and challenges for future research.

Similar content being viewed by others

Statistical inference links data and theory in network science

The anatomy of a population-scale social network

Intrinsic dimension as a multi-scale summary statistics in network modeling

Introduction.

In many scientific fields, researchers study phenomena best characterized at the systems level 1 . To understand such phenomena, it is often insufficient to focus on the way individual components of a system operate. Instead, one must also study the organization of the system’s components, which can be represented in a network 2 . The value of analysing the structure of a system in this way has been underscored by the advent of network science, which has delivered important insights into diverse sets of phenomena studied across the sciences 3 , 4 . This Primer discusses methodology to apply this line of reasoning to the statistical analysis of multivariate data.

Network approaches involve the identification of system components (network nodes) and the relations among them (links between nodes). Well-known examples include semantic networks (in which concepts are connected through shared meanings 5 ), social networks (in which people are connected through acquaintance 6 ) and neural networks (in which neurons are connected through axons 7 ). After nodes and links are identified, and a network has been constructed, one can study its topology using descriptive tools of network science 8 . For instance, one can describe the global topology of a network (such as a small-world network or random graph 9 ) or the position of individual nodes within the network (for example, by assessing node centrality 10 ). These analyses are often carried out with the goal of relating structural features of the network to system dynamics 4 , 11 .

Network representations have a long history as research tools in statistics, where they encode important information concerning the joint probability distribution of a set of variables 12 . For instance, in graphical models, unconnected nodes are conditionally independent given all or a subset of other nodes in the network 12 ; in causal models, graphical criteria are used to determine whether parameters in an estimated causal model are identified 13 ; and in structural equation models, path-tracing rules on network representations are used to determine the value of empirical correlations implied by the model 14 .

In this Primer, we present network analysis of multivariate data as a method that combines both multivariate statistics and network science to investigate the structure of relationships in multivariate data. This approach identifies network nodes with variables and links between nodes and describes them with statistical parameters that connect these variables (for example, partial correlations). Statistical models are used to assess the parameters that define the links in the network, in a process known as network structure estimation . Then, using a process of network description , the resulting network is characterized using the tools of network science 15 , 16 , 17 . Here, we refer to this combined procedure of network structure estimation and network description as psychometric network analysis (Fig.  1 ).

Joint probability distribution of multivariate data characterized in terms of conditional associations and independencies. Conditional independencies translate into disconnected nodes; conditional associations translate into links between nodes, typically weighted by the strength of the association. The resulting structure is subsequently described and analysed as a network.

Network approaches to multivariate data can be used to advance several different goals. First, they can be used to explore the structure of high-dimensional data in the absence of strong prior theory on how variables are related. In these analyses, psychometric network analysis complements existing techniques for the exploratory analysis of psychological data, such as exploratory factor analysis (which aims to represent shared variance due to a small number of latent variables) and multidimensional scaling (which aims to represent similarity relations between objects in a low-dimensional metric space). The unique focus of psychometric network analysis is on the patterns of pairwise conditional dependencies that are present in the data. Second, network representations can be used to communicate multivariate patterns of dependency effectively, because they offer powerful visualizations of patterns of statistical association. Third, network models can be used to generate causal hypotheses, as they represent statistical structures that may offer clues to causal dynamics; for instance, networks that represent conditional independence relations form a gateway that connects correlations to causal relations 13 , 18 , 19 .

Here, we review these functions of network analysis in the context of three types of application in psychological science, illustrating them with examples taken from personality, attitude research and mental health.

Experimentation

The schematic workflow of psychometric network analysis as discussed in this paper is represented in Fig.  2 . Typically, one starts with a research question that dictates a data collection scheme, which includes cross-sectional designs, time-series designs and panel designs. Psychometric network analysis begins with node selection , a choice primarily driven by substantive rather than methodological considerations. The core of the psychometric network analysis methodology then lies in the steps of network structure estimation, network description and network stability analysis . Importantly, inferences drawn from the output of network analytic methods require both substantive domain knowledge and general methodological considerations regarding the stability and robustness of the estimated network in order to optimally inform scientific inference.

The heart of the psychometric network analysis methodology described lies in the steps of network structure estimation (to construct the network), network description (to characterize the network) and network stability analysis (to assess the robustness of results). These steps are informed by substantive research questions and data collection procedures. Output of the network approaches combines with general methodological considerations and domain-specific knowledge to support scientific inference.

Network approaches to multivariate data are based on generic statistical procedures and thus invite applications to many types of data. The approaches discussed in this paper, however, have been developed and typically used in the context of psychometric variables such as responses to questionnaire items, symptom ratings and cognitive test scores 20 , possibly extended with background variables such as age and gender 21 , genetic information 22 , physiological markers 23 , medical conditions 24 , experimental interventions 25 and anticipated downstream effects 26 . Accordingly, the nodes we discuss will ordinarily represent items and tests.

The majority of network modelling approaches use conditional associations to define the network structure prevalent in a set of variables 20 , 27 . A conditional association between two variables holds when these variables are probabilistically dependent, conditional on all other variables in the data. Which measure of conditional association to use depends on the structure of the data; for instance, for multivariate normal data, partial correlations would be indicated, whereas for binary data, logistic regression coefficients may be used. The strength of this conditional association is typically represented in the network as an edge weight that describes the connection between two nodes. If the association between two variables can be explained by other variables in the network, so that their conditional association vanishes when these other variables are controlled for, then the corresponding nodes are disconnected in the network representation.

The description of the joint probability distribution of a set of variables in terms of pairwise statistical interactions is a graphical model 12 known as the pairwise Markov random field (PMRF) 27 . Versions of the PMRF are known under several other names as well in the statistical literature; see refs 28 , 29 for an overview of the relations between relevant statistical models. Many network modelling approaches attempt to estimate the PMRF, typically using existing statistical methodologies such as significance testing 30 , cross-validation 31 , information filtering 32 and regularized estimation 16 , 33 , 34 , 35 , 36 . Because of its prominence in the literature, this Primer is limited to network approaches that use the PMRF, although it should be noted that other approaches to the analysis of multivariate data exist, including models based on zero-order associations 37 , self-reported causal relations between variables 38 , 39 and relative importance of variables 40 .

Because, in typical multivariate data, a substantive subset of associations between variables vanishes upon conditioning, applications of network modelling generally return non-trivial topological structures and the description of such structures is an important goal of psychometric network analysis. For instance, the extent to which network nodes are connected and the network’s general topology are of interest, as well as the position of individual nodes in that structure. Thus, psychometric network analysis typically involves interpreting the output of statistical estimation procedures, for example an estimated PMRF, as the input for network description techniques taken from network science (Fig.  1 ).

Types of data

Network models always operate on associations among sets of variables, but such associations can be extracted from many different experimental and quasi-experimental designs. We focus on three designs that represent typical data environments in social science where psychometric network analysis can be relevant: cross-sectional networks, longitudinal networks of panel data and time-series networks (Fig.  3 ).

Typical data types include cross-sectional, panel and time-series data.

Cross-sectional data

In applications to cross-sectional data, networks are representations of the conditional associations between variables measured at a single time point in a large sample ( T  = 1, N  = large). In this case, the associations between variables are driven by individual differences, which renders such networks useful for studying the psychometric structure of psychological tests 29 . In the cross-sectional data example used here, we are interested in the empirical relations among personality and personal goals. We analyse a data set in which three levels of personality structure are assessed via questionnaires, using network models to investigate empirical relations among these elements and personal goals. Our illustrative personality data set features 432 observations and 39 variables of interest 41 .

We represent network structures as they arise at different levels of aggregation 42 at which personality can be described. These can be higher-order traits, such as conscientiousness ; facets , such as orderliness, industriousness and impulse control 43 ; or even specific single items, such as prudent, reflective and disciplined (items of impulse control 44 ) that allow for a finer distinction of personality characteristics below facets (see ref. 45 for an example). The objective of psychometric network analysis, in this case, would be to offer insight into the multivariate pattern of conditional dependencies that characterize the joint distribution of these variables at these different levels of aggregation (Box  1 ).

When cross-sectional data are analysed through network estimation and interpreted via network description, is it important to keep in mind that resulting topologies represent structures that describe differences between individuals, and that these are not necessarily isomorphic to processes or mechanisms that characterize the individuals who make up the data. That is, inter-individual differences do not necessarily translate to intra-individual processes 46 , 47 . If one is interested solely in the structure of individual differences, cross-sectional data are adequate, but research into intra-individual dynamics ideally complements such data sources with panel data or time series.

Box 1 Psychometric structure of personality test scores

A substantial part of the literature on human personality is concerned with the psychometric structure of personality tests. Research has shown that people’s self-ratings on adjectives (such as outgoing, punctual and nervous) or responses to items that characterize them (I make friends easily, I get stressed out easily; see the International Personality Item Pool for an overview of psychometric items) show systematic patterns of correlations. These patterns of correlations are often described by a low-dimensional factor model; most often, solutions with five factors known as the Five Factor Model 142 or with six factors known as HEXACO 143 are proposed. The factors in the Five Factor Model are often interpreted as latent variables that cause the correlations between the item scores. However, attempts to ground these latent variables in psychological or biological theories of human functioning have met with limited success, and correlations between personality items may have other causes that include content overlap and the presence of direct relations between properties measured by these items 69 . Such hypotheses are consistent with the finding that items in personality scales typically either load on several factors simultaneously or feature correlated residuals, suggesting that the latent variable model does not fully account for the correlations between item scores. Recently, network models have been proposed as an alternative representation of the psychometric structure of personality tests that does not require a priori commitment to a particular generating model (such as a latent variable model) and may serve to identify alternative mechanisms that lead to correlations between items 44 , 144 . An exploratory factor model and a network model are visualized in the figure using IPIP-Big Five Factor Markers open data 145 .

In network applications to longitudinal data (also referred to as panel data), a limited set of repeated measurements characterize both the association structure of variables at a given time point and the way these conditional dependencies’ change over time ( N  >  T ). Such measures can illuminate the structure of individual differences and intra-individual change in parallel.

In our example for network approaches to panel data, we use repeated assessments of emotions and beliefs towards Bill Clinton as represented in longitudinal panel data of the American National Election Studies (ANES) between 1992 and 1996. We aim to model consistency, stability and extremity of attitudes towards Bill Clinton during the time that he transitioned from governor of Arkansas to president of the United States. The network theory of attitudes (Box  2 ) formalizes changes in attitude importance as network temperature , for example, increasing or decreasing interdependence between attitude elements. In the panel data example, network analyses can assist in modelling temperature changes in the interdependence of attitude elements towards BillClinton.

Box 2 Causal attitude network model and attitudinal entropy

The network theory of attitudes holds that attitudes are higher-level properties emerging from lower-level beliefs, feelings and behaviours 111 . A negative attitude towards a politician might emerge from negative beliefs (that the politician is incompetent and bad for the future of the country), feelings (anger and frustration towards the politician) and behaviours (voting behaviour and making jokes about the politician). These different attitude elements can be modelled as nodes in a network, in which edges between attitude elements represent potentially bidirectional interactions between the elements. The network theory of attitudes relies on the central principle that interdependence between attitude elements increases when the attitude is important to the person and when an individual directs attention to the attitude object 111 . This theory uses analogical modelling of statistical mechanics and the effect of attitude importance, and attention is formalized as a decrease in temperature. The effect of decreasing network temperature is that the entropy of a multivariate system decreases by making (attitude) elements in the system more interdependent. In the case of attitudes, this effect translates to heightened consistency and stability of the attitude when it is important, because the different attitude elements rein each other in under low temperature compared with high temperature (see the figure, parts a and b ). Low temperature leads to low variance of the overall attitude within an individual, and hence higher stability. By contrast, a group of individuals with low-temperature attitude networks have higher variance than a high-temperature group, because the pressure of attitude elements to align leads to higher extremity of the overall attitude, creating a bimodal distribution. As this bimodal distribution only occurs in a low-temperature/high-importance scenario, the network model offers a potential explanation for polarization: higher importance leads to more strongly connected networks, which in turn produces polarized attitudes.

Time-series data

Networks as applied to time-series data of one or multiple persons characterize multivariate dependencies between time series of variables that are assessed intra-individually ( T  = large, N  ≥ 1). Such networks are most often applied in situations where one seeks insight into the dynamic structure of systems. For instance, in the social and clinical sciences, recent years have witnessed a surge of daily diary studies and ecological momentary assessment , conducted via smartphones and designed to study such dynamic structures. Studies typically measure experiences — such as mood states, symptoms, cognitions and behaviours — at the moment they occur 48 , 49 . In such cases, network analyses can assist in interpreting intensive longitudinal data by offering insightful characterizations of the multivariate pattern of dynamics.

In the time-series data example used here, we leverage data gathered during the onset of the COVID-19 pandemic to investigate the impact of reduced social contact due to lockdown measures on the mental health of students enrolled at Leiden University in the Netherlands. In this ecological momentary assessment study, students were followed daily for 2 weeks, assessing momentary social contact as well as current stress, anxiety and depression 4 times per day via a smartphone application 50 . In this situation, a network model can be fitted to these data to investigate to what degree social contact variables influence mental health variables over the course of hours and days. Because, in this case, multiple individuals were assessed multiple times, the design is mixed; in such situations, it is often profitable to use a statistical multilevel approach 27 , 51 , in which the repeated observations are treated as nested in the individuals. This explicitly separates individual differences from time dynamics 52 .

In a PMRF, the joint likelihood of multivariate data is modelled through the use of pairwise conditional associations, leading to a network representation that is undirected. There are several benefits to the PMRF that make this particular network representation important. First, the PMRF encodes conditional independence relations (in terms of absent links between nodes), which form an important gateway to identify candidate data-generating mechanisms 29 , 53 , 54 . However, the PMRF does not require an a priori commitment to any particular data-generating mechanism (unlike directed acyclic graph estimation or latent variable modelling, for example). Because PMRFs do not place strong assumptions on the structure of the generating model but do hold clues to causal structure through conditional independencies, they are well suited to exploratory analyses (see also Limitations and optimizations). In addition, estimated PMRFs often describe the data successfully with only a subset of the possible parameters (for example, using sparse network structures), which leads to more insightful network visualizations. Finally, a priori commitments invariably lead to problems of underdetermination , because many structurally different models will produce indistinguishable data, which is known as statistical equivalence. By contrast, the PMRF is uniquely identified, so there are no two equivalent PMRFs with different parameters that fit the data equally well.

If data are continuous, a popular type of PMRF is the Gaussian graphical model (also known as a partial correlation network) in which edges are parameterized as partial correlation coefficients 55 , 56 . If data are binary, a popular PMRF developed to estimate the Ising model can be used, in which edges are parameterized as log-linear relationships 16 , 29 , 36 . The Ising model and the Gaussian graphical model can be combined in mixed graphical models , in which edges are parameterized as regression coefficients from generalized linear regression models 57 . Mixed graphical models represent the most general approach to PMRF estimation and also allow for the inclusion of categorical and count variables.

The PMRF can readily be estimated from cross-sectional data, in which case it can be reasonably assumed that all cases or rows in the data set — which usually represent people — are independent. This assumption is violated, however, in panel data and time-series designs, in which an individual case is not a person but, rather, a single measurement moment of one of the persons in the sample. In this case, violations of independence occur in two ways: temporal dependencies are introduced owing to the temporal aspect of data gathering (for example, a person who feels sad at 12:00 might still feel sad at 15:00), and responses from the same person may correlate more strongly with one another than responses between different persons (for example, a person might feel, on average, very sad in all responses). Thus, whereas cross-sectional data can use independence assumptions that allow for the application of population-sample logic, time-series data require a model to deal with the dependence between data points.

To address time dependencies, PMRFs may be extended with temporal effects that represent regressions on the previous time point in a single-person case. These temporal effects may, for instance, be estimated through the application of a vector autoregressive model. The structure of the associations that remain after taking temporal effects into account can also be represented in a PMRF. This network is typically designated as the contemporaneous network . Thus, in contrast to the case of cross-sectional networks, the application of network modelling to multivariate time series returns separate network structures to characterize the dependence relation describing associations that link variables through time, and associations that link variables after these temporal effects have been taken into account. These networks have a distinct function in the interpretation of results. The temporal network can be read in terms of carry-over effects at the timescale defined by the spacing between repeated measures, where the temporal ordering can also assist causal interpretation. The contemporaneous network will include associations that are due to effects that occur at different timescales rather than those defined by the spacing between repeated measurements. Note that, just as cross-sectional networks, time-series networks almost always represent correlational data; interpretation of such networks in causal terms is never straightforward.

In panel data or N  >1 time-series settings, multilevel modelling can differentiate between within-person and between-person variance In addition to the temporal and contemporaneous networks (both of which represent within-person information), one then obtains a third structure of associations that can be characterized as a PMRF. This third structure represents the conditional associations between the long-term averages of the time series between people. This structure, similar to that of cross-sectional networks, represents associations driven by individual differences and is known as the between-persons network. Thus, in the cross-sectional case one obtains one network (the PMRF of the association between individual differences), in the time-series case one obtains two networks (the directed temporal network of vector autoregressive coefficients and the undirected contemporaneous network of the regression residuals) and for multiple time series and panel data one obtains three networks (temporal and contemporaneous networks driven by intra-individual processes and the between-persons network driven by individual differences). In addition, one may use multiple time series to identify network structures that are (in)variant over individuals 58 or that define subgroups 59 .

Edge selection

Methods of edge selection are based on general statistical theory as applied to the estimation of conditional associations. Three methods are featured in the literature. First, approaches based on model selection through fit indices can be used. For example, regularized estimation procedures 16 , 33 lead to models that balance parsimony and fit, in the sense that they aim to only include edges that improve the fit of the network model to data (for instance, by minimizing the extended Bayesian information criterion 35 ). Second, null hypothesis testing procedures are used to evaluate each individual edge for statistical significance 30 ; if desired, this process can be specialized to deal with multiple testing, through Bonferroni correction or false discovery rate approaches, for example. Last, cross-validation approaches can be used. In these approaches, the network model is chosen based on its performance in out of sample prediction, such as in k -fold cross-validation 31 .

Network description

Once a network structure is estimated, network description tools from network science can be applied to investigate the topology of PMRF networks 3 , 60 .

Global topologies that are particularly important revolve around the distinction between sparse versus dense networks. In sparse networks, few (if any) edges are present relative to the total number of possible edges. In dense networks, the converse holds, and relatively many edges are present. This distinction is important for two reasons. First, optimal estimation procedures may depend on sparsity, for example regularization-based approaches can be expected to perform well if data are generated from a sparse network, but may not work well in dense networks. Second, in sparse networks the importance of individual nodes is typically more pronounced, because in dense networks all nodes tend to feature a similar large number of edges. Further analyses can be used to investigate the global topology of the network structure in greater detail; for example, Dalege et al. 61 investigate small-world features 9 of attitude networks and Blanken et al. 62 use clique percolation methodology to assess the structure of psychopathology networks. Although network visualizations are typically based on aesthetic principles — for example, by using force-based algorithms 63 — recently, techniques have been proposed to visualize networks based on multidimensional scaling 64 . These techniques allow node placement to mirror the strength of conditional associations in the PRMF, so that more strongly connected nodes are placed in closer vicinity to each other.

Local topological properties of networks feature attributes of particular nodes or sets of nodes. For example, measures of centrality can be used to investigate the position of nodes in the network. The most commonly used centrality metrics are node strength, which sums the absolute edge weights of edges per node; closeness, which quantifies the distance between the node and all other nodes by averaging the shortest path lengths to all other nodes; and betweenness, which quantifies how often a node lies on the shortest path connecting any two other nodes 65 . These metrics are directly adapted from social network analysis, and can be used to assess the position of variables in the network representation constructed by the researchers. Strength conveys how strongly the relevant variable is conditionally associated with other variables in the network, on average. However, note that closeness and betweenness treat association as distances, which can be problematic. More recently, new measures have been introduced, specifically designed for the analysis of PMRF structures. Expected influence is a measure of centrality that takes the sign of edge weights into account 66 ; this can be appropriate when variables have a non-arbitrary coding, such as when the high values of all variables indicate more psychopathology. Predictability quantifies how much variance in a node is explained by its neighbours 54 , which can be used to assess the extent to which the network structure predicts node states. Further extensions to the characterization of networks and nodes in terms of network science involve participation coefficients, minimal spanning trees and clique percolation as proposed by Letina et al. 67 and Blanken et al. 62 . Finally, the shortest paths between nodes may yield insight into the strongest predictive pathways, and clustering in the network may yield insight into potential underlying unobserved causes and the dimensionality of the system 68 .

Applications

Although network approaches as discussed here draw on insights from statistics and network theory, the specific combination of techniques discussed in this paper has its roots in psychometric modelling in psychological contexts. This section discusses three areas in which this approach has been particularly successful. First, the domain of personality research, where network models have been applied to describe the interaction between stable behavioural patterns that characterize an individual. Second, the domain of attitude research, in which networks have been designed to model the interaction between attitude elements (feelings, thoughts and behaviours) to explain phenomena such as polarization . Last, the domain of mental health research, where networks have been used to represent disorders as systems of interacting symptoms and to represent key concepts such as vulnerability and resilience.

Personality research

Personality researchers are interested in examining the processes characterizing personality traits 69 . One type of these processes is motivational: research shows that traits such as conscientiousness or extraversion can be considered as means to achieve specific goals, for example getting tasks done and having fun, which have been identified as goals relevant for conscientiousness and extraversion, respectively 70 . Psychometric network analysis of personality traits and motivational goals combined offers a novel way to explore relations among relatively stable dispositions. Personality networks can represent personality at different levels of abstraction, from higher-order traits to facets to specific items. One could wonder which abstraction level should be preferred. The answer requires balancing simplicity and accuracy of predictions and of explanations. Focusing on a level that is too abstract might result in losing important details, whereas adding elements beyond necessary could result in noisy estimates and, thus, faulty conclusions. An approach that can help is out of sample predictability 71 . We illustrate this by reanalysing data from Costantini et al. 41 (Study 3) that include 9 goals identified as relevant for conscientiousness and 30 items from an adjective-based measure of conscientiousness that assess three main facets: industriousness, impulse control and orderliness 44 .

Data and analysis

In this sample ( N  = 432) we explored how well we could predict goals using a tenfold cross-validation approach 72 . The networks depicted in Fig.  4 represent Gaussian graphical models estimated with the qgraph R package 15 , using graphical lasso regularization. The lambda parameter for graphical lasso was selected through the extended Bayesian information criterion (γ = 0.5 (ref. 33 )). We varied the level of representation of the personality dimensions from general (single trait) to specific (3 facets) to molecular (30 items) and explored the relationships between personality and 9 goal scores.

Network of relationships between motivational goals (yellow) and conscientiousness at the level of the trait (panel a ), its facets (panel b ) and items (panel c ). Blue edges represent positive connections and red edges represent negative connections; thicker edges represent stronger relationships. Relationships between personality and goals are emphasized with saturated colours. *Items reverse-scored before entering network estimation. d | Strength centrality for each goal in each network.

The results depicted in Fig.  4a suggest that some goals are positively associated and some negatively associated with an overall conscientiousness score. Two goals, personal realization (node 3) and be safe (node 7), do not show direct connections to the trait. However, this network does not consider several ways in which one can be conscientious. Some people can be more organized, others can be more controlled and yet others can be more industrious 43 . The facet-level network (Fig.  4b ) shows that most goals are related to a specific subset of one or two of the three facets, thus characterizing more clearly specific portions of the trait. At this level, personal realization (node 3) is positively related to industriousness but negatively connected to the remaining facets, something that would not have been apparent had we considered the trait level exclusively. At the item level (Fig.  4c ), connections appear generally consistent with those emerging at the facet level, albeit with some exceptions. For example, avoid or manage things you do not care about (node 6) shows relations with items of orderliness, whereas no such connection emerged at the facet level.

Figure  4d shows strength centrality estimates for all nodes in the three networks. Irrespective of the abstraction level considered, the most central goal was do something well, avoid mistakes (node 4). The centrality of node 4 is due to connections to other goals, rather than to its connections to conscientiousness. Such connections suggest that node 4 might serve as a means for several other goals. For example, one could speculate that doing things well might be important in the pursuit of more abstract goals, such as personal realization (node 3) or having control (node 2) (see ref. 72 for a discussion of the abstractness of these goals).

Results show that the trait level is never the best level for prediction and that some goals are best predicted at the item level and others at the facet level (Table  1 ), albeit in one case (goal 16) the trait level performed better than the item level. In general, specific levels might be useful if one is mainly interested in examining which elements of the personality system drive the association with a criterion 73 or if one is purely interested in prediction. In our example, the item level performed, on average, slightly better than the facet level in terms of prediction, although this was not the case for all goals (see also ref. 74 ). A preference for more abstract levels sometimes amounts to sacrificing a small portion of prediction in exchange for a noticeable gain in theoretical simplicity. Furthermore, using abstract predictors can sometimes assuage multicollinearity. At the same time, abstracting too much can lump together concepts that are better understood separately. There is no ultimate answer to the selection of the best abstraction level in personality as it heavily depends on the questions being asked and the data available. In general, the facet level might often provide a good balance between specificity and simplicity 75 , 76 .

Attitude research

Social psychologists are interested in how beliefs and attitudes can change over time. We illustrate the use of networks to improve our understanding of these processes with a study of attitudes towards Bill Clinton in the United States in the early 1990s. Based on the network theory of attitudes (Box  2 ) one expects that temperature should decrease throughout the years, because Bill Clinton was probably more on individuals’ minds when he was president than before he was president. We investigate changes in the network structure of these attitudes in the years before and during his presidency and whether the temperature of the attitude network changes. In this example, we estimate temperature using variations in how strongly correlated the attitude elements are at the different time points. Temperature of attitude networks can, however, also be measured by several proxies, such as how much attention individuals direct towards a given issue and how important they judge the issue.

We use data from the open access repository of the ANES between 1992 and 1996 including beliefs and emotions towards Bill Clinton. For this example, the presented data have been previously reported 77 , 78 . Beliefs were assessed using a four-point scale ranging from describes Bill Clinton extremely well to not at all. Emotions were assessed using a dichotomous scale with answer options of yes, have felt and no, never felt. Dichotomizing the belief questions, we fit an Ising model with increasing constraints representing their hypotheses to this longitudinal assessment of beliefs and emotions in the American electorate. We investigate the impact on the fit of the model of constraining edges between nodes to be equal across time points, constraining the external fields to be equal across time points and constraining the temperature (the entropy of the system) to be equal across time points. Additionally, we tested whether a dense network (all nodes are connected) or a sparse network (at least some edges are absent) fits the data best. After estimating the network, we applied the walktrap algorithm to the network to detect different communities, such as, for example, sets of highly interconnected nodes 68 , 79 . The walktrap algorithm makes use of random walks to detect communities. If random walks between two nodes are sufficiently short, these two nodes are assigned to the same community.

The results show a sparse network with a stable network structure, where edges do not differ between time points (Fig.  5 ). The model with varying external information and temperature fitted the data best. Figure  5a shows the estimated network at the four time points. The attitude network is connected: every attitude element is at least indirectly connected to every other attitude element. As can be seen, negative emotions of feeling afraid and angry are strongly connected to each other, as are positive emotions of feeling hope and pride. Within the beliefs, believing that Bill Clinton gets things done and provides strong leadership are closely connected. The belief that he cares about people is closely connected to the positive emotions. The walktrap algorithm detected two communities: one large community that contains all beliefs and the positive emotions; and one smaller community that contains the negative emotions. This indicates that positive emotions are more closely related to (positive) beliefs than positive and negative emotions are related to each other.

a | Estimated attitude network towards Bill Clinton. Colour of nodes corresponds to communities detected by the walktrap algorithm. Blue edges indicate positive connections between attitude elements and red edges indicate negative connections; width of the edges corresponds to strength of connection. b | Change in temperature throughout time. c | Histograms for overall attitude towards Bill Clinton in each year.

Figure  5b shows changes in temperature throughout the years. As can be expected from the network theory of attitudes (Box  2 ), the temperature of the attitude network generally decreased throughout the years, with the sharpest drop before the election in 1996 revealing an increase in the specificity of respondents’ attitudes towards Clinton. This implies that attitude elements became more consistent over time, resulting in more polarized attitudes. The increase in temperature between 1993 and 1994, however, is somewhat surprising.

Figure  5c shows the distribution of the overall attitude, separately measured on a scale ranging from 0 to 100, with higher numbers indicating more favourable attitudes. Based on the decreasing temperature of the attitude networks, a corresponding increase in the extremity of these distributions is to be expected. This is exactly what was found; the variance of the distributions increased in a somewhat similar fashion as the temperature of the attitude network decreased. The increase in the variance between 1993 and 1994 was the only exception.

Mental health research

Mental health research and practice rest on reportable symptoms and observable signs. Therapists interviewing patients will ask questions about subjective symptoms as well as assess signs of behavioural distress (such as agitated hand-wringing and crying). The challenge for both mental health researchers and therapists is to determine the cause of the person’s constellation of signs and symptoms. Therapists, moreover, have the additional charge of using this information to devise an appropriate course of treatment. The network theory of psychopathology 80 , 81 suggests that mental disorders are best understood as clusters of symptoms sufficiently unified by causal relations among those symptoms that support induction, explanation, prediction and control 82 , 83 (Box  3 ). Signs and symptoms are constitutive of disorder, not the result of an unobservable common cause. We illustrate this with an example study of social interaction and its relations to mental health variables in a student sample during the COVID-19 pandemic.

Box 3 Disease models versus network structures in mental health

Symptoms and signs associated with mental illness do not co-occur randomly. For example, recurrent obsessive thoughts about potential contamination co-occur more often with compulsive handwashing than with paranoid delusions. The tendency for some symptoms to co-occur may be owing to a common underlying cause. For example, consider a patient complaining of fatigue, pain upon swallowing, a fever and white patches in the throat. A physician may posit the Streptococcus bacterium as the common cause of the co-occurrence of the patient’s signs and symptoms 86 , 87 , and can eliminate the patient’s illness by therapeutically targeting the bacteria rather than the resulting symptoms. This bacterial model of disease became firmly entrenched early in psychiatry’s history, shaping the field’s methods and motivating researchers to identify the common underlying cause of regularly co-occurring signs and symptoms 81 (see the figure, part a ). Despite the widespread and often implicit influence of the bacterial model of disease, failures to discover biomarkers of putative underlying entities have continued to mount during the past century 146 . The network theory of psychopathology provides an alternative account of why some symptoms tend to co-occur 37 , 80 . Rather than being the independent, functionally unrelated consequences of an underlying common cause, the network theory of psychopathology posits that symptoms co-occur owing to causal interactions among the signs and symptoms themselves 81 , 147 (see the figure, part b ). Indeed, the Diagnostic and Statistical Manual of Mental Disorders criteria often specify functional relations among symptoms. For example, compulsive rituals diminish the distress provoked by obsessions and avoidance behaviour in panic disorder arises as a consequence of recurrent panic attacks. This simple idea forms the foundation of the network approach to psychopathology and motivates the effort to investigate the structure of relationships among symptoms using psychometric network analysis.

Researchers have devised an ecological momentary assessment study following 80 students (mean age = 20.38 years, standard deviation = 3.68, range = 18–48 years; n  = 60 female, n  = 19 male, n  = 1 other) from Leiden University for 2 weeks in their daily lives 50 . With 19 different nationalities represented, this sample is highly international. Most students are single ( n  = 50), one–third of the students are currently employed and about 1 in 5 students report prior mental health problems. In this study, participants are asked about the extent of their worry, sadness, irritability and other subjective phenomenological experiences four times per day via a smartphone application. We use multilevel vector autoregressive modelling to assess the contemporaneous and temporal associations among problems related to generalized anxiety and depression. As a reminder, the contemporaneous network covers relations within the same 3-h assessment window, and the temporal network lag – 1 relations between one 3-h window and the next.

The resulting networks can be used to inform our understanding of how the modelled variables evolve over time (Fig.  6 ). In this application, the model suggests that the cognitive symptom worry and the affective symptom nervous exhibit a strong contemporaneous association but do not exhibit a conditional dependence relation in temporal analyses, indicating that the relation between these items may be limited to a 3-h time interval. Similarly, we can clarify the paths by which external factors, such as social interaction, predict and are predicted by mental health. For example, the contemporaneous association between offline social interaction (nodes 8) and worry (node 3) occurs via feelings of loneliness (node 7), information which could be used in the generation of hypotheses about the causal relationships among these symptoms. It is also notable that different types of social interaction are differentially associated with loneliness. Offline social interaction is conditionally associated with lower levels of loneliness, whereas online social interaction is associated with higher levels of loneliness. The temporal associations further inform our understanding of these relationships. Difficulty envisioning the future and difficulty relaxing predict online social interaction, and online social interaction predicts subsequent difficulty relaxing. This illustrates how psychometric network analysis of time series naturally leads to more detailed hypotheses about the system under study; do note that this use of network analysis is exploratory and that generated hypotheses require independent testing, ideally through research that utilizes experimental interventions.

Contemporaneous network (left) of conditional associations between variables obtained after controlling for temporal effects in the temporal network (right); latter represents carry-over effects from one time point to the next. Blue edges indicate positive connections and red edges indicate negative connections; width of edges corresponds to strength of connection.

Network analyses not only equip researchers to investigate the associations among symptoms but also provide a novel framework for conceptualizing treatment. There are at least two potential ways one can intervene on a system, such as that depicted in Fig.  6 . First, we can lower the mean level of a node by diminishing its frequency or severity. For example, we could intervene on the online social interaction node, hoping, based on the contemporaneous relations, that it might promote offline social interaction, alleviate loneliness and, in turn, foster less worry, more optimism and greater interest and pleasure. However, even if initially successful, merely intervening on a node may be insufficient, leaving the person vulnerable to relapse, as the structure of the network remains intact. If pessimism and an inability to relax are, indeed, encouraging online social interaction, then when our intervention on this node ceases, the problem may return, erasing our treatment gains. Accordingly, instead of targeting a specific node (or symptom), we may target the link between symptoms, thereby changing the structure of the network. For example, rather than aiming to reduce online social interaction in general, we could specifically target the tendency to engage in online social interaction when the person experiences pessimism or difficulty relaxing, thereby eliminating the temporal association between these symptoms and online social interaction and disrupting the network.

Reproducibility and data deposition

A challenge posed by the estimation of PMRFs from multivariate data is that estimation error and sampling variation need to be taken into account when interpreting the network model. For example, networks estimated from two different groups of people may look different visually but this difference may be due to sampling variation. Several statistical methods have been proposed for assessing the stability and accuracy of estimated parameters as well as to compare network models of different groups. For many statistical estimators, data resampling techniques such as bootstrapping and permutation tests have been developed for this purpose 17 , 84 .

Standard approaches to robustness analyses involve three targets: individual edge weight estimates, differences between edges in the network and topological metrics defined on the network structure, such as node centrality. The robustness of edge weight estimates can be assessed by constructing intervals that reflect the sensitivity of edge weight estimates to sampling error, such as confidence intervals, credibility intervals and bootstrapped intervals (Fig.  7a ). The robustness of differences between edge weights can be assessed by investigating to what degree the bootstrapped intervals for the relevant coefficients overlap (Fig.  7b ). The robustness of network properties such as node centrality can be investigated through a case-dropping bootstrap, in which progressively fewer cases are sampled from the original data set to obtain subsamples; the correlation between centrality measures in these subsamples and the total sample is plotted as a function of the size of the subsamples (Fig.  7c ). Various approaches are available to assess these forms of robustness, including approaches based on bootstrapping 17 and Bayesian statistics 85 .

a | Sample value (red line), bootstrapped 95% intervals (shaded area) and average bootstrapped value (blue line) of edge weights. b | Whether the 95% bootstrapped interval of the differences between any two edges includes the value zero (grey squares) or not (dark squares) gives an indication of whether two edges are different from each other 17 . Diagonal visualizes magnitude of original edge; red indicates negative values, blue indicates positive values and colour saturation indicates absolute values (more saturated the colour, stronger the edge). c | Results of case-dropping bootstrap analysis showing average correlation between strength centrality estimated in the full sample and strength estimated on a random subsample, retaining only a certain portion of cases (from 90% to 10%). Shaded area indicates 95% bootstrapped confidence intervals of correlation estimates. Higher values indicate better stability of centrality estimates 17 .

The generalizability of network structures can be assessed by comparing results in different samples. This is typically assessed by examining the similarity of network structures across samples. A formal test for the invariance of networks has been developed to assess the null hypothesis that the networks are identical at the level of the population from which individuals have been sampled 84 and Bayesian analyses 86 can also be used to assess invariance of networks. Finally, moderated network analysis 87 and multi-group analysis have been introduced as methods for statistically comparing groups 88 . To gain more insight into the degree to which pairwise associations correspond across networks, the correlation between edge weights in different groups can be inspected.

It should be emphasized that, owing to sampling variability, one should not ordinarily expect to reproduce the network completely, and that the degree to which the network structure replicates depends on several factors, including the network architecture itself 80 , 89 . For this reason, network analysts have developed tools to compute the expected reproducibility of network structure estimation results 27 . Figure  8 displays the expected replicability of one of the personality networks reported above that one should expect, if the estimated networks were the true networks, using different sample sizes. For instance, from this analysis it is apparent that the item-level network should be expected to replicate less strongly than the facet-level and trait-level networks.

ReplicationSimulator generates multiple data sets from an estimated network to assess expected sensitivity (probability of including edges given that they are, in fact, present in the generating network) and specificity (probability of leaving out edges given that they are, in fact, absent in the generating network) as well as expected correlation between edge weights for two replication data sets generated from the network.

In addition to sampling variability, network structures can be affected by random measurement error. The effects of measurement error differ depending on the type of network estimated. In cross-sectional networks, ignoring measurement error typically leads to an underestimation of network density. If the strength of edges is associated with the network structure itself, this may lead to an artificial magnification of network structure. In longitudinal and time-series networks, however, measurement error can also lead to spurious edges 90 . One way to deal with measurement error is to utilize latent variable modelling; in this case, the network model is augmented with a measurement model that relates multiple observables to a single latent node, and the PMRF is estimated at the level of these latent nodes 27 .

To improve standardization and reproducibility, recent research explicates minimal shared norms in reporting psychological network analyses 91 . For methods sections of scientific papers, such norms include information on subsample and variable selection, the presence of deterministic relations between variables and skip structures that may distort the network, the estimation methods used as well as any additional specifications (such as thresholding, regularization, parameter settings), how the accuracy and stability of edge estimates were assessed and, finally, the statistical software and packages used, including their versions (Table  2 ).

In terms of results, current norms recommend reporting the final sample size after handling missing data, plotting and visualization choices and the accuracy and stability checks of any network model, in light of the research question of the researcher. If the research questions concern centrality estimates, case-drop bootstrap results would be reported, for example. Many reporting routines are dependent on the specific research goals of the researcher and different analysis routines result in different reporting choices. Burger et al. 91 elaborate on these routines and further discuss important considerations for network analysis and potential sources of misinterpretation of network structures.

Limitations and optimizations

Network structure estimation.

Although many network structures are now estimable through standard software, some limitations still remain. First, although treatments of dichotomous, unordered categorical and continuous data and their combinations are well developed 57 , treatments of ordinal data are still suboptimal. Ongoing research is developing approaches for such data, which are common in the social sciences 92 , 93 . Second, estimation routines have traditionally used nodewise regularized regression 16 or the graphical lasso 33 . Although these techniques return visually attractive networks, statistically they are most appropriate when networks can be expected to be sparse 35 , 36 . Non-regularized estimation approaches based on model selection provide an important alternative, as research suggests that they can outperform regularized approaches in several situations 94 , 95 . Third, many network modelling techniques handle missing data suboptimally, for example through list-wise deletion. Emerging estimation frameworks use alternative approaches, which allow for better missing data handling, for instance through full-information maximum likelihood 88 , 96 .

Interpretation

The fact that, in psychometric network models, edges are not observed but estimated necessitates the evaluation of sampling variance, which requires extensions. First, current techniques for edge selection do not guarantee that unselected edges are statistically indistinguishable from zero or that evidence for their absence is strong. Relatedly, many current estimation methods do not produce standard errors or confidence intervals around edge weight estimates, as the sampling distributions of regularized regression coefficients are unwieldy. This limits the interpretation of individual edges. In non-regularized networks, significance tests can be used, but this practice is not based on model selection and therefore inherits problems inherent in significance testing. New Bayesian approaches address these challenges, as they can quantify evidence for or against edge inclusion 97 .

Second, network structures depend on which variables are included. Nodes that are highly central in one network may therefore be peripheral in another. In addition, if important nodes are missing, this can affect the structure of the network; for instance, it may lead to increased edge strengths among nodes that represent effects of an omitted common cause 98 . If nodes are essentially duplicates of each other — for example, if two nodes have topological overlap — this will influence the network architecture as well 99 , 100 . Thus, network interpretation depends on a judicious choice of which variables to include in the network, and more research is needed to develop theoretical frameworks to guide these choices.

Third, centrality metrics have been suggested to reflect the importance of nodes to the system that the network represents 33 and early literature interpreted nodes with high centrality as more plausible targets for intervention 101 . However, recent work has highlighted situations where centrality is not a good proxy for causal influence 102 , 103 , and for certain networks, peripheral nodes may be more important in determining system behaviour 104 . In addition, in some areas such as psychopathology, interactions may occur at different timescales, which complicates the relation between association structure and causal dynamics. This has rendered the use of centrality measures a topic of debate, with some papers arguing that, because psychometric network models do not specify dynamics or flow, centrality metrics should not be interpreted in terms of causal dynamics at all. In addition, centrality metrics that concatenate paths between nodes (such as closeness and betweenness) are based on (absolute) conditional associations; these do not represent physical distances — they violate transitivity — and should not be interpreted as such. Finally, although network software indexes many types of centrality, including closeness, betweenness, degree, strength, eigenvalue and expected influence, there are no clear guidelines on which interpretations are licensed by each of these 105 , so more research is needed to investigate the relation between theoretical properties of possible generating models and empirical estimates of centrality 106 .

Causal inference

The constituent parts of PMRFs are purely statistical associations, so that direct causal inference based on network structures is not justified. Although the PMRF itself is typically unique — there are no alternative PMRFs that will generate the same set of joint probability distributions — the correspondence between the PMRF and generative causal systems is one to many: edges between nodes may arise owing to directed causal effects or feedback loops, but also owing to unobserved common causes 107 , conditioning on common effects 102 , 108 and various other structures (Fig.  9 ). As is the case for causal inference in general, causal inference based on PMRFs requires the statistical structure to be augmented by substantively backed assumptions 53 . This motivates the articulation of strong network theories in addition to the development of network models, as for instance have been devised for intelligence 109 , 110 , attitudes 61 , 111 and certain mental disorders 112 .

Pairwise Markov random field (PMRF) (left) can be generated by alternative models (middle) that have different interpretations (right). Dashed lines represent range of models and interpretations not captured here.

Current directions in network estimation may assist in causal inference by developing better methodologies. For example, causal search algorithms may be effective in identifying a particular causal model in certain cases 18 , 113 , 114 , 115 . In addition, inclusion of interventions in network structures may facilitate causal interpretation 25 , 116 , 117 . Alternatively, researchers may revert to non-causal interpretation of network structures. In such cases, marginal associations can be preferred over conditional associations if the goal is purely to describe the patterns of association. For example, Schwaba et al. 118 opted to model a network of correlations rather than partial correlations, because of the descriptive nature of their goal.

Confirmatory testing

Most applications of network analysis use exploratory techniques to estimate network structures 20 . However, advances in network estimation allow one to constrain parameters (such as edge weights) to a specific value, constrain edges to have the same edge weight as each other or constrain edge weights to be equal across different groups 88 , 119 . The ability to test these constraints adds confirmatory data analysis approaches to the network analytic toolbox 120 . The psychonetrics R package 121 is an example of an implementation that allows for confirmatory testing of network constraints. There are also Bayesian implementations available for testing constraints in networks that can be used to test whether an edge is positive, negative or null, and to test order constraints on edge weights 85 .

One way of arriving at network hypotheses is on the basis of exploratory network analyses. For example, an initial data set may be used to estimate a network model exploratively. In the next step, all of the estimated zeros are included as constraints in a network model that is fitted to a new data set 122 . Similarly, one can use an exploratively estimated network to formulate different hypotheses about the order of the strengths of edge weights and test these hypotheses against each other using Bayes factors 123 . A second way of arriving at network hypotheses is from substantive theory about the phenomena being modelled, from which network structures implied by the theory can be deduced 124 . To test substantive hypotheses, future methodological research should provide tools that can help researchers express substantive hypotheses in constraints on network structures, which can subsequently be tested using confirmatory models.

Network models are suited to estimate and represent patterns of conditional associations without requiring strong a priori assumptions on the generating model, which renders them well suited to exploratory data analysis and visualization of dependency patterns in multivariate data. As statistical analysis methods, the software routines for estimating, visualizing and analysing networks enhance existing exploratory data analysis methods, as they focus specifically on the patterns of pairwise conditional associations between variables. The resulting network representation of conditional associations between variables, as encoded in the PMRF, may be of interest in its own right, but can also function as a gateway that allows the researcher to assess the plausibility of different generating models that may produce the relevant conditional associations. This assessment may include latent variable models 29 and directed acyclic graphs 115 in addition to explanations based on network theories 80 , 123 .

Because network models for multivariate data explicitly represent pairwise interactions between components in a system, they form a natural bridge from data analysis to theory formation based on network science principles 3 . In this respect, networks not only accommodate the multivariate architecture of systems but also offer a toolbox to develop formal theories of the dynamical processes that form and maintain them 61 , 124 . One successful example of such an approach is the mutualism model of intelligence 125 , which proposes an explanation of the positive correlations between intelligence tests based on network concepts. This explanation quantifies how the structure of the cognitive network impacts the dynamic processes taking place in it. This model has been extended to explain various empirical phenomena reported in the intelligence literature 126 , 127 . Similar developments have taken place in clinical psychology 112 , 128 and attitude research 78 , as featured in the current paper.

The combination of network representations in data analytics and theory formation is remarkably fruitful in forging connections between different fields and research programmes. One important connection is that between the study of inter-individual differences and intra-individual mechanisms. More than half a century ago, Cronbach famously diagnosed psychological science to be a deeply divided discipline 129 . With one camp of psychological scientists concerned with mechanistic explanations and another camp primarily focused on the study of individual differences, that dichotomy is still prevailing. Some argue that in order to overcome this division, psychological scientists should rethink their widespread practice of detaching statistical practice from substantive theory 130 , 131 , 132 . One reason for this detachment, however, has been the long-standing lack of an intuitive modelling framework that facilitates both theory construction and process-based computations and simulation, so that it can connect the two disciplines 129 . But this gap is exactly what makes network approaches fall on fertile soil. Networks readily accommodate the multivariate architecture of psychological systems and also offer a toolbox to develop formal theories of the dynamical processes that act on them. In this manner, models of intra-individual dynamics can serve as explanations of systems of inter-individual differences, bridging the gap between intra-individual and inter-individual modelling 129 .

Network models are not only useful to create bridges from data analysis to theory formation but also to connect different scientific disciplines to each other. In recent years, network science and associated complex systems approaches have led to an active interdisciplinary research area in which researchers from many fields collaborate. Network approaches in psychology, as discussed here, have similarly broadened the horizon of relevant candidate methodologies relevant to psychological research questions; for instance, it is remarkable that the first network model fitted to psychopathology data 16 was based on modelling approaches developed to study atomic spins 133 , 134 , whereas subsequent studies into the research dynamics of psychopathology 135 investigated sudden transitions using methodology developed in ecology 136 and, finally, recent studies of interventions in such networks are based on control theory 137 . Clearly, network representations create a situation where scientists with different disciplinary backgrounds find a common vocabulary.

This common vocabulary creates tantalizing possibilities for building bridges between research areas — particularly in cases where the systems studied are plausibly constituted by networks operating at different levels, such as human behaviour. For instance, largely independent of one another, neuroscience and psychology have both developed research traditions rooted in network science. With network models of the brain based on neuroimaging studies and network models of psychological responses, the bigger picture might no longer be obstructed by disciplinary fences 138 , 139 . This promise is by no means limited to psychology and its subdisciplines; the network fever is spanning many disciplines, such as physics, ecology and biology. In fact, the best cited network papers are concerned with universal network characteristics that can advance interdisciplinary theory and modelling 9 , 140 . We have only begun to chart the connections between disciplines that deal with complex networks, and we hope that network approaches to multivariate data can play a productive role in this respect.

Code availability

Code and data used in sample analyses are available from https://github.com/DennyBorsboom/NatureMethodsPrimer_NetworkAnalysis .

Change history

21 february 2022.

A Correction to this paper has been published: https://doi.org/10.1038/s43586-022-00101-1

Meadows, D. H. Thinking in Systems: A Primer (Chelsea Green, 2008). This text is the most convincing to motivate systems thinking throughout the sciences .

Barabási, A. L. The network takeover. Nat. Phys. 8 , 14–16 (2012).

Article   Google Scholar  

Newman, M. E. J. Networks: An Introduction (Oxford University Press, 2010). This text is an ideal introduction to network science and the associated mathematical modelling techniques .

Newman, M. E. J., Barabási, A. L. E. & Watts, D. J. The Structure and Dynamics of Networks (Princeton University Press, 2006).

Richens, R. H. Preprogramming for mechanical translation. Mech. Transl. Comput. Ling. 3 , 20–25 (1956).

Google Scholar  

Milgram, S. The small world problem. Psychol. Today 2 , 60–67 (1967).

Ramón y Cajal, S. The Croonian Lecture: la fine structure des centres nerveux. Proc. R. Soc. Lond. 55 , 444–468 (1894).

Newman, M. E. & Clauset, A. Structure and inference in annotated networks. Nat.Commun. 7 , 1–11 (2016).

Watts, D. J. & Strogatz, S. H. Collective dynamics of ‘small-world’ networks. Nature 393 , 440–442 (1998). This article kickstarts the growth of network science in the past few decades .

Article   ADS   MATH   Google Scholar  

Bavelas, A. A mathematical model for group structures. Appl. Anthropol. 7 , 16–30 (1948).

Kolaczyk, E. D. Statistical Analysis of Network Data: Methods and Models (Springer, 2009). This text is an authoritative overview of statistical models for network analysis .

Cox, D. R. & Wermuth, N. Multivariate Dependencies: Models, Analysis and Interpretation Vol. 67 (CRC, 1996).

Pearl, J. Causality: Models, Reasoning, and Inference (Cambridge University Press, 2000). This crucial book makes the connection between conditional independence patterns and causal structures .

Wright, S. Correlation and causation. J. Agric. Res. 20 , 557–585 (1921).

Epskamp, S., Cramer, A. O., Waldorp, L. J., Schmittmann, V. D. & Borsboom, D. qgraph: network visualizations of relationships in psychometric data. J. Stat. Softw. 48 , 1–18 (2012).

Van Borkulo, C. D. et al. A new method for constructing networks from binary data. Sci. Rep. 4 , 1–10 (2014). This paper is the first application of regularized network modelling in psychopathology .

Epskamp, S., Borsboom, D. & Fried, E. I. Estimating psychological networks and their accuracy: a tutorial paper. Behav. Res. Methods 50 , 195–212 (2018). This article introduces robustness analysis for network modelling .

Spirtes, P., Glymour, C. N., Scheines, R. & Heckerman, D. Causation, prediction, and search (MIT Press, 2000).

Haslbeck, J., Ryan, O., Robinaugh, D., Waldorp, L. & Borsboom, D. Modeling psychopathology: from data models to formal theories. Psychol. Methods https://doi.org/10.31234/osf.io/jgm7f (2021).

Robinaugh, D. J., Hoekstra, R. H., Toner, E. R. & Borsboom, D. The network approach to psychopathology: a review of the literature 2008–2018 and an agenda for future research. Psychol. Med. 50 , 353–366 (2020).

Deserno, M. K., Borsboom, D., Begeer, S. & Geurts, H. M. Multicausal systems ask for multicausal approaches: a network perspective on subjective well-being in individuals with autism spectrum disorder. Autism 21 , 960–971 (2017).

Isvoranu, A. M. et al. Toward incorporating genetic risk scores into symptom networks of psychosis. Psychol. Med. 50 , 636–643 (2020).

Fried, E. et al. Using network analysis to examine links between individual depressive symptoms, inflammatory markers, and covariates. Psychol. Med. 16 , 2682–2690 (2019).

Isvoranu, A. M. et al. Extended network analysis: from psychopathology to chronic illness. BMC Psychiatry 21 , 1–9 (2021).

Blanken, T. F. et al. Introducing network intervention analysis to investigate sequential, symptom-specific treatment effects: a demonstration in co-occurring insomnia and depression. Psychother. Psychosom. 88 , 52–54 (2019).

Blanken, T. F., Borsboom, D., Penninx, B. W. & Van Someren, E. J. Network outcome analysis identifies difficulty initiating sleep as a primary target for prevention of depression: a 6-year prospective study. Sleep 43 , zsz288 (2020).

Epskamp, S. Psychometric network models from time series and panel data. Psychometrika 85 , 206–231 (2020). This article systematizes psychometric network models for longitudinal data .

Article   MathSciNet   MATH   Google Scholar  

Kindermann, R. P. & Snell, J. L. On the relation between Markov random fields and social networks. J. Math. Sociol. 7 , 1–13 (1980).

Marsman, M. et al. An introduction to network psychometrics: relating Ising network models to item response theory models. Multivar. Behav. Res. 53 , 15–35 (2018). This article establishes systematic links between network models and latent variable analysis .

Williams, D. R. & Rast, P. Back to the basics: rethinking partial correlation network methodology. Br. J. Math. Stat. Psychol. 73 , 187–212 (2020).

Haslbeck, J. M. & Waldorp, L. J. How well do network models predict observations? On the importance of predictability in network models. Behav. Res. Methods 50 , 853–861 (2018).

Christensen, A. P., Kenett, Y. N., Aste, T., Silvia, P. J. & Kwapil, T. R. Network structure of the Wisconsin Schizotypy Scales — short forms: examining psychometric network filtering approaches. Behav. Res. Methods 50 , 2531–2550 (2018).

Epskamp, S. & Fried, E. I. A tutorial on regularized partial correlation networks. Psychol. Med. 23 , 617 (2018).

Costantini, G. et al. Stability and variability of personality networks. A tutorial on recent developments in network psychometrics. Pers. Individ. Differ. 136 , 68–78 (2019).

Barber, R. F. & Drton, M. High-dimensional Ising model selection with Bayesian information criteria. Electron. J. Stat. 9 , 567–607 (2015).

Ravikumar, P., Wainwright, M. J., Raskutti, G. & Yu, B. High-dimensional covariance estimation by minimizing ℓ1-penalized log-determinant divergence. Electron. J. Stat. 5 , 935–980 (2011). This seminal article presents regularized estimation of network structure .

Borsboom, D. & Cramer, A. O. Network analysis: an integrative approach to the structure of psychopathology. Annu. Rev. Clin. Psychol. 9 , 91–121 (2013).

Frewen, P. A., Allen, S. L., Lanius, R. A. & Neufeld, R. W. Perceived causal relations: novel methodology for assessing client attributions about causal associations between variables including symptoms and functional impairment. Assessment 19 , 480–493 (2012).

Deserno, M. K. et al. Highways to happiness for autistic adults? Perceived causal relations among clinicians. PLoS ONE 15 , e0243298 (2020).

Robinaugh, D. J., LeBlanc, N. J., Vuletich, H. A. & McNally, R. J. Network analysis of persistent complex bereavement disorder in conjugally bereaved adults. J. Abnorm. Psychol. 123 , 510–522 (2014).

Costantini, G., Saraulli, D. & Perugini, M. Uncovering the motivational core of traits: the case of conscientiousness. Eur. J. Pers. 34 , 1073–1094 (2020).

Deserno, M. K., Borsboom, D., Begeer, S. & Geurts, H. M. Relating ASD symptoms to well-being: moving across different construct levels. Psychol. Med. 48 , 1179–1189 (2018).

Roberts, B. W., Lejuez, C., Krueger, R. F., Richards, J. M. & Hill, P. L. What is conscientiousness and how can it be assessed? Dev. Psychol. 50 , 1315–1330 (2014).

Costantini, G. et al. Development of indirect measures of conscientiousness: combining a facets approach and network analysis. Eur. J. Pers. 29 , 548–567 (2015).

Mõttus, R., Kandler, C., Bleidorn, W., Riemann, R. & McCrae, R. R. Personality traits below facets: the consensual validity, longitudinal stability, heritability, and utility of personality nuances. J. Pers. Soc. Psychol. 112 , 474–490 (2017).

Molenaar, P. C. A manifesto on psychology as idiographic science: bringing the person back into scientific psychology, this time forever. Measurement 2 , 201–218 (2004). This article establishes the need for time-series modelling of psychometric data .

Hamaker, E. L., Kuiper, R. M. & Grasman, R. P. A critique of the cross-lagged panel model. Psychol. Methods 20 , 102–116 (2015). This article demonstrates the need to separate between-subject from within-subject structures in the analysis of longitudinal data .

aan het Rot, M., Hogenelst, K. & Schoevers, R. A. Mood disorders in everyday life: a systematic review of experience sampling and ecological momentary assessment studies. Clin. Psychol. Rev. 32 , 510–523 (2012).

Moskowitz, D. S. & Young, S. N. Ecological momentary assessment: what it is and why it is a method of the future in clinical psychopharmacology. J. Psychiatry Neurosci. 31 , 13 (2006).

Fried, E. I., Papanikolaou, F. & Epskamp, S. (2021). Mental health and social contact during the COVID-19 pandemic: an ecological momentary assessment study. Clin. Psychol. Sci. https://doi.org/10.1177/21677026211017839 (2021).

Bringmann, L. F. et al. A network approach to psychopathology: new insights into clinical longitudinal data. PLoS ONE 8 , e60188 (2013). This article introduces multilevel time-series modelling in the context of psychopathology networks .

Article   ADS   Google Scholar  

Hamaker, E. L., Ceulemans, E., Grasman, R. P. P. P. & Tuerlinckx, F. Modeling affect dynamics: state of the art and future challenges. Emot. Rev. 7 , 316–322 (2015).

Pearl, J. Causal inference. Causality: objectives and assessment. Proc. Mac. Learn. Res. 6 , 39–58 (2010).

Spirtes, P., Glymour, C. N., Scheines, R. & Heckerman, D. Causation, Prediction, and Search (MIT Press, 2000).

Chen, B., Pearl, J. & Kline, R. Graphical tools for linear path models. Psychometrika 4 , R432 (2018).

Roverato, A. & Castelo, R. The networked partial correlation and its application to the analysis of genetic interactions. J. R. Stat. Soc. 66 , 647–665 (2017).

Article   MathSciNet   Google Scholar  

Haslbeck, J. & Waldorp, L. J. mgm: estimating time-varying mixed graphical models in high-dimensional data. Preprint at https://arxiv.org/abs/1510.06871 (2020). This article generalizes the network model to mixed data types .

Gates, K. M. & Molenaar, P. C. M. Group search algorithm recovers effective connectivity maps for individuals in homogeneous and heterogeneous samples. NeuroImage 63 , 310–319 (2012).

Gates, K. M., Lane, S. T., Varangis, E., Giovanello, K. & Guskiewicz, K. Unsupervised classification during time-series model building. Multivar. Behav. Res. 52 , 129–148 (2017).

Barabasi, A. L. Network Science (Cambridge University Press, 2018). This text is an authoritative overview of network science .

Dalege, J. et al. Toward a formalized account of attitudes: the causal attitude network (CAN) model. Psychol. Rev. 123 , 2 (2016).

Blanken, T. F. et al. The role of stabilizing and communicating symptoms given overlapping communities in psychopathology networks. Sci. Rep. 8 , 1–8 (2018).

Fruchterman, T. M. & Reingold, E. M. Graph drawing by force-directed placement. Software Pract. Exper. 21 , 1129–1164 (1991).

Jones, P. J., Mair, P. & McNally, R. J. Visualizing psychological networks: a tutorial in R. Front. Psychol. 9 , 1742 (2018).

Opsahl, T., Agneessens, F. & Skvoretz, J. Node centrality in weighted networks: generalizing degree and shortest paths. Soc. Netw. 32 , 245–251 (2010). This article generalizes network metrics to weighted networks as intensively used in current network approaches to multivariate data .

Robinaugh, D. J., Millner, A. J. & McNally, R. J. Identifying highly influential nodes in the complicated grief network. J. Abnorm. Psychol. 125 , 747 (2016).

Letina, S., Blanken, T. F., Deserno, M. K. & Borsboom, D. Expanding network analysis tools in psychological networks: minimal spanning trees, participation coefficients, and motif analysis applied to a network of 26 psychological attributes. Complexity https://doi.org/10.1155/2019/9424605 (2019).

Golino, H. F. & Epskamp, S. Exploratory graph analysis: a new approach for estimating the number of dimensions in psychological research. PLoS ONE 12 , e0174035 (2017).

Baumert, A. et al. Integrating personality structure, personality process, and personality development. Eur. J. Pers. 31 , 503–528 (2017).

McCabe, K. O. & Fleeson, W. Are traits useful? Explaining trait manifestations as tools in the pursuit of goals. J. Pers. Soc. Psychol. 110 , 287–301 (2016).

Yarkoni, T. & Westfall, J. Choosing prediction over explanation in psychology: lessons from machine learning. Perspect. Psychol. Sci. 12 , 1100–1122 (2017).

Costantini, G., Perugini, M. & Mõttus, R. A framework for testing causality in personality research. Eur. J. Pers. 32 , 254–268 (2018).

Mõttus, R. Towards more rigorous personality trait—outcome research. Eur. J. Pers. 30 , 292–303 (2016).

Mõttus, R. et al. Descriptive, predictive and explanatory personality research: different goals, different approaches, but a shared need to move beyond the Big Few traits. Eur. J. Pers. 34 , 1175–1201 (2020).

Paunonen, S. V. & Ashton, M. C. Big five factors and facets and the prediction of behavior. J. Pers. Soc. Psychol. 81 , 524 (2001).

Paunonen, S. V. & Ashton, M. C. On the prediction of academic performance with personality traits: a replication study. J. Res. Pers. 47 , 778–781 (2013).

Dalege, J., Borsboom, D., van Harreveld, F., Waldorp, L. J. & van der Maas, H. L. Network structure explains the impact of attitudes on voting decisions. Sci. Rep. 7 , 1–11 (2017).

Dalege, J., Borsboom, D., van Harreveld, F. & van der Maas, H. L. A network perspective on attitude strength: testing the connectivity hypothesis. Soc. Psychol. Personal. Sci. 10 , 746–756 (2019).

Pons, P. & Latapy, M. Computing communities in large networks using random walks. J. Graph. Algorithms Appl. 10 , 191–218 (2006).

Borsboom, D. A network theory of mental disorders. World Psychiatry 16 , 5–13 (2017).

McNally, R. Network analysis of psychopathology: controversies and challenges. Annu. Rev. Clin. Psychol. 17 , 31–53 (2020). This paper is a state-of-the-art overview of the status of network analysis in psychopathology .

Kendler, K. S., Zachar, P. & Craver, C. What kinds of things are psychiatric disorders? Psychol. Med. 41 , 1143–1150 (2011).

Held, B. S. The distinction between psychological kinds and natural kinds revisited: can updated natural-kind theory help clinical psychological science and beyond meet psychology’s philosophical challenges? Rev. Gen. Psychol. 21 , 82–94 (2017).

Van Borkulo, C. D., et al. Comparing network structures on three aspects: a permutation test (preprint). https://doi.org/10.13140/RG.2.2.29455.38569 (2017).

Williams, D. R. & Mulder, J. Bayesian hypothesis testing for Gaussian graphical models: conditional independence and order constraints. J. Math. Psychol. 99 , 102441 (2020). This article introduces Bayesian approaches to hypothesis testing in network models .

Williams, D. R., Piironen, J., Vehtari, A. & Rast, P. Bayesian estimation of Gaussian graphical models with predictive covariance selection. Preprint at https://arxiv.org/abs/1801.05725 (2018).

Haslbeck, J. M., Borsboom, D. & Waldorp, L. J. Moderated network models. Multivariate Behav. Res. 56 , 256–287 (2019).

Epskamp, S., Isvoranu, A. M. & Cheung, M. Meta-analytic Gaussian network aggregation. Psychometrika https://doi.org/10.1007/s11336-021-09764-3 (2021).

Article   MATH   Google Scholar  

Williams, D. R. Learning to live with sampling variability: expected replicability in partial correlation networks. (preprint). PsyArXiv https://doi.org/10.31234/osf.io/fb4sa (2020).

Schuurman, N. K. & Hamaker, E. L. Measurement error and person-specific reliability in multilevel autoregressive modeling. Psych. Methods 24 , 70 (2019).

Burger, J. et al. Reporting standards for psychological network analyses in cross-sectional data. (preprint). PsyArXiv https://doi.org/10.31234/osf.io/4y9nz (2020).

Isvoranu, A. & Epskamp, S. Continuous and ordered categorical data in network psychometrics: which estimation method to choose? deriving guidelines for applied researchers. (preprint). PsyArXiv https://doi.org/10.31234/osf.io/mbycn (2021).

Johal, S. K. & Rhemtulla, M. Comparing estimation methods for psychometric networks with ordinal data. (preprint). PsyArXiv https://doi.org/10.31234/osf.io/ej2gn (2021).

Williams, D. R., Rhemtulla, M., Wysocki, A. C. & Rast, P. On nonregularized estimation of psychological networks. Multivariate Behav. Res. 54 , 719–750 (2019).

Wysocki, A. C. & Rhemtulla, M. On penalty parameter selection for estimating network models. Multivariate Behav. Res. 56 , 288–302 (2019).

Mansueto, A. C., Wiers, R., van Weert, J., Schouten, B. C. & Epskamp, S. Investigating the feasibility of idiographic network models. (preprint). PsyArXiv https://doi.org/10.31234/osf.io/hgcz6 (2020).

Williams, D. R., Briganti, G., Linkowski, P. & Mulder, J. On accepting the null hypothesis of conditional independence in partial correlation networks: a Bayesian analysis. (preprint). PsyArXiv https://doi.org/10.31234/osf.io/7uhx8 (2021).

Hallquist, M. N., Wright, A. G. & Molenaar, P. C. Problems with centrality measures in psychopathology symptom networks: why network psychometrics cannot escape psychometric theory. Multivariate Behav. Res. 56 , 199–223 (2019).

Christensen, A. P., Golino, H. & Silvia, P. J. A psychometric network perspective on the validity and validation of personality trait questionnaires. Eur. J. Pers. 34 , 1095–1108 (2020).

Fried, E. I. & Cramer, A. O. Moving forward: challenges and directions for psychopathological network theory and methodology. Perspect. Psychol. Sci. 12 , 999–1020 (2017).

Rhemtulla, M. et al. Network analysis of substance abuse and dependence symptoms. Drug Alcohol. Depend. 161 , 230–237 (2016).

Dablander, F. & Hinne, M. Node centrality measures are a poor substitute for causal inference. Sci. Rep. 9 , 1–13 (2019).

Spiller, T. R. et al. On the validity of the centrality hypothesis in cross-sectional between-subject networks of psychopathology. BMC Med. 18 , 1–14 (2020).

Quax, R., Apolloni, A. & Sloot, P. M. The diminishing role of hubs in dynamical processes on complex networks. J. R. Soc. Interface 10 , 20130568 (2013).

Bringmann, L. F. et al. What do centrality measures measure in psychological networks? J. Abnorm. Psychol. 128 , 892 (2019).

Borgatti, S. P. Centrality and network flow. Soc. Netw. 27 , 55–71 (2005).

Rohrer, J. M. Thinking clearly about correlations and causation: graphical causal models for observational data. Adv. Methods Pract. Psychol. Sci. 1 , 27–42 (2018).

de Ron, J., Fried, E. I. & Epskamp, S. Psychological networks in clinical populations: investigating the consequences of Berkson’s bias. Psychol. Med. 51 , 168–176 (2021).

Kan, K. J., van der Maas, H. L. & Levine, S. Z. Extending psychometric network analysis: empirical evidence against g in favor of mutualism? Intelligence 73 , 52–62 (2019).

Kievit, R. A. et al. Mutualistic coupling between vocabulary and reasoning supports cognitive development during late adolescence and early adulthood. Psychol. Sci. 28 , 1419–1431 (2017).

Dalege, J., Borsboom, D., van Harreveld, F. & van der Maas, H. L. The attitudinal entropy (AE) framework as a general theory of individual attitudes. Psychol. Inq. 29 , 175–193 (2018). This article develops the network theory of attitudes .

Robinaugh, D. et al. Advancing the network theory of mental disorders: a computational model of panic disorder. (preprint). PsyArXiv https://doi.org/10.31234/osf.io/km37w (2020). This article is the first to augment symptom network models with substantively plausible formalized theory .

Scutari, M. Learning Bayesian networks with the bnlearn R package. J. Stat. Softw. 35 , 1–22 (2010).

Colombo, D. & Maathuis, M. H. Order-independent constraint-based causal structure learning. J. Mach. Learn. Res. 15 , 3741–3782 (2014).

MathSciNet   MATH   Google Scholar  

Ryan, O., Bringmann, L. F. & Schuurman, N. K. The challenge of generating causal hypotheses using network models. (preprint). PsyArXiv https://doi.org/10.31234/osf.io/ryg69 (2020).

Kossakowski, J. J., Gordijn, M. C. M., Harriette, R. & Waldorp, L. J. Applying a dynamical systems model and network theory to major depressive disorder. Front. Psychol. 10 , 1762 (2019).

Mooij, J. M., Magliacane, S. & Claassen, T. Joint causal inference from multiple contexts. J. Mach. Learn. Res. 21 , 1–108 (2020).

Schwaba, T., Rhemtulla, M., Hopwood, C. J. & Bleidorn, W. A facet atlas: visualizing networks that describe the blends, cores, and peripheries of personality structure. PLoS ONE 15 , e0236893 (2020).

Drton, M. & Richardson, T. S. in Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence (UAI ‘04) 130–137 (AUAI Press, 2004).

Epskamp, S., Rhemtulla, M. & Borsboom, D. Generalized network psychometrics: combining network and latent variable models. Psychometrika 82 , 904–927 (2017).

Epskamp, S. Psychonetrics: structural equation modeling and confirmatory network analysis. Psychonetrics http://psychonetrics.org/ (2020).

Kan, K. J., de Jonge, H., van der Maas, H. L., Levine, S. Z. & Epskamp, S. How to compare psychometric factor and network models. J. Intell. 8 , 35 (2020).

Rodriguez, J. E., Williams, D. R., Rast, P. & Mulder, J. On formalizing theoretical expectations: Bayesian testing of central structures in psychological networks. (preprint). PsyArXiv https://doi.org/10.31234/osf.io/zw7pf (2020).

Cramer, A. O., Waldorp, L. J., Van Der Maas, H. L. & Borsboom, D. Comorbidity: a network perspective. Behav. Brain Sci. 33 , 137 (2010).

Van Der Maas, H. L. et al. A dynamical model of general intelligence: the positive manifold of intelligence by mutualism. Psychol. Rev. 113 , 842 (2006). This article contains the first articulation of a network model to account for patterns of individual differences in psychology .

Savi, A. O., Marsman, M., van der Maas, H. L. & Maris, G. K. The wiring of intelligence. Perspect. Psychol. Sci. 14 , 1034–1061 (2019).

Van Der Maas, H. L., Kan, K. J., Marsman, M. & Stevenson, C. E. Network models for cognitive development and intelligence. J. Intell. 5 , 16 (2017).

Cramer, A. O. et al. Major depression as a complex dynamic system. PloS ONE 11 , e0167490 (2019).

Cronbach, L. J. [1957]. The two disciplines of scientific psychology. Am. Psychol. 12 , 671 (2016).

Gigerenzer, G. Personal reflections on theory and psychology. Theor. Psychol. 20 , 733–743 (2010).

Wood, D., Gardner, M. H. & Harms, P. D. How functionalist and process approaches to behavior can explain trait covariation. Psychol. Rev. 122 , 84 (2015).

Borsboom, D., van der Maas, H. L., Dalege, J., Kievit, R. A. & Haig, B. D. Theory construction methodology: a practical framework for building theories in psychology. Perspect. Psychol. Sci. 16 , 756–766 (2021).

Lenz, W. Beitrag zum Verständnis der magnetischen Erscheinungen in festen Körpern [German]. Physikalische Z. 21 , 613–615 (1920).

Ising, E. Beitrag zur theorie des ferromagnetismus [German]. Z. für Phys. 31 , 253–258 (1925).

Wichers, M., Groot, P. C. & Psychosystems, E. S. M., EWS Group. Critical slowing down as a personalized early warning signal for depression. Psychother. Psychosom. 85 , 114–116 (2016). This article is the first to investigate early warnings in psychopathology transitions .

Scheffer, M. et al. Early-warning signals for critical transitions. Nature 461 , 53–59 (2009). This crucial article articulates the link between complex systems, sudden transitions and early warning signals in time series .

Henry, T. R., Robinaugh, D. & Fried, E. I. On the control of psychological networks. (preprint). PsyArXiv https://doi.org/10.31234/osf.io/7vpz2 (2021).

Brooks, D. et al. The multilayer network approach in the study of personality neuroscience. Brain Sci. 10 , 915 (2020).

Bathelt, J., Geurts, H. M. & Borsboom, D. More than the sum of its parts: merging network psychometrics and network neuroscience with application in autism. Preprint at bioRxiv https://doi.org/10.1101/2020.11.17.386276 (2020).

Liljeros, F., Edling, C. R., Amaral, L. A. N., Stanley, H. E. & Åberg, Y. The web of human sexual contacts. Nature 411 , 907–908 (2001).

R Core Team. R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, 2020).

McCrae, R. R. & Costa, P. T. Jr. in Sage Handbook of Personality Theory and Assessment Vol. 1 273–294 (Sage, 2008).

Ashton, M. C. & Lee, K. Objections to the HEXACO model of personality structure—and why those objections fail. Eur. J. Pers. 34 , 492–510 (2020).

Cramer, A. O. J. et al. Dimensions of normal personality as networks in search of equilibrium: you can’t like parties if you don’t like people. Eur. J. Pers. 26 , 414–431 (2012).

Goldberg, L. R. et al. The international personality item pool and the future of public-domain personality measures. J. Res. Pers. 40 , 84–96 (2006).

McNally, R. J. What is Mental Illness? (Belknap Press of Harvard University Press, 2011).

Borsboom, D. Psychometric perspectives on diagnostic systems. J. Clin. Psychol. 64 , 1089–1108 (2008).

Download references

Acknowledgements

D.J.R.’s work on this manuscript was supported by a National Institute of Mental Health (NIMH) Career Development Award (K23-MH113805). M.K.D.’s work was supported by a Rubicon fellowship of the Netherlands Organization for Scientific Research (NWO) (no. 019.191SG.005). D.B.’s work was supported by European Research Council Consolidator Grant 647209. M.P. and G.C.’s work was supported by European Union’s Horizon 2020 research and innovation programme (grant no. 952464). E.I.F. is supported by funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant no. 949059). S.E. is supported by NWO Veni (grant number 016-195-261). C.D.v.B.’s work was supported by European Research Council Consolidator Grant 647209, granted to D.B. J.D.’s work was supported by an EU Horizon 2020 Marie Curie Global Fellowship (no. 889682). The content is solely the responsibility of the authors and does not necessarily represent the views of the funding agencies.

Author information

Authors and affiliations.

Department of Psychology, University of Amsterdam, Amsterdam, Netherlands

Denny Borsboom, Sacha Epskamp, Adela-Maria Isvoranu, Claudia D. van Borkulo & Lourens J. Waldorp

Center for Lifespan Psychology, Max Planck Institute for Human Development, Berlin, Germany

Marie K. Deserno

Department of Psychology, University of California, Davis, CA, USA

Mijke Rhemtulla & Anna C. Wysocki

University of Amsterdam, Centre for Urban Mental Health, Amsterdam, Netherlands

Sacha Epskamp & Claudia D. van Borkulo

Department of Clinical Psychology, Leiden University, Leiden, Netherlands

Eiko I. Fried

Department of Psychology, Harvard University, Cambridge, MA, USA

Richard J. McNally

Department of Psychiatry, Massachusetts General Hospital & Harvard Medical School, Boston, MA, USA

Donald J. Robinaugh

Department of Psychology, University of Milan Bicocca, Milan, Italy

Marco Perugini & Giulio Costantini

Santa Fe Institute, Santa Fe, NM, USA

Jonas Dalege

Center for Philosophy of Science, University of Pittsburgh, Pittsburgh, PA, USA

Riet van Bork

You can also search for this author in PubMed   Google Scholar

Contributions

Introduction (D.B. and M.K.D.); Experimentation (D.B., M.K.D., E.I.F. and C.D.v.B.); Results (D.B., M.K.D., S.E., A.-M.I. and L.J.W.); Applications (D.B., M.K.D., E.I.F., R.J.M., D.J.R., M.P., J.D. and G.C.); Reproducibility and data deposition (D.B., M.K.D. and G.C.); Limitations and optimizations (D.B., M.K.D., M.R., R.v.B. and A.C.W.); Outlook (D.B. and M.K.D.); Overview of the Primer (D.B. and M.K.D.).

Corresponding author

Correspondence to Denny Borsboom .

Ethics declarations

Competing interests.

The authors declare no competing interests.

Additional information

Peer review information.

Nature Reviews Methods Primers thanks D. Hevey, S. Letina, M. Southward and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Related links

International Personality Item Pool: https://ipip.ori.org/

IPIP-Big Five Factor Markers open data: https://openpsychometrics.org/_rawdata/IPIP-FFM-data-8Nov2018.zip

A generic term that subsumes a family of measures that aim to assess how central a node is in a network topology, such as node strength, betweenness and closeness.

The application of statistical models to assess the structure of pairwise (conditional) associations in multivariate data.

Characterization of the global network topology and the position of individual nodes in that topology.

The analysis of multivariate psychometric data using network structure estimation and network description.

The choice of which variables will function as nodes in the network model.

The assessment of estimation precision and robustness to sampling error of psychometric networks.

A statistical association between two variables that does not vanish when taking into account other variables that may explain the association.

In psychometric network analysis, edge weights typically are parameter estimates that represent the strength of the conditional association between nodes.

(PMRF). An undirected network that represents variables as nodes and conditional associations as edges, in which unconnected nodes are conditionally independent.

A generic term to characterize networks in terms of their global topology, for instance in terms of density or architecture.

A term used in personality research to designate the propensity to be self-controlled, responsible, hardworking and orderly and to follow rules. In most models of human personality, conscientiousness is considered a high-order factor.

Specific traits subsumed by a factor in hierarchically organized models of personality. For instance, orderliness and industriousness are facets of conscientiousness.

A parameter of network models that controls the entropy of node state patterns. A network with low temperature will allow only node states that align, such that positively connected nodes must be in the same state and negatively connected nodes must be in the opposite state, whereas a network with high temperature will allow more random patterns of activation.

Daily diary methodology to measure psychological states and behaviours in the moment, for instance by using ambulatory assessment devices such as mobile phones to administer questionnaires that probe how the person feels or what the person does at that specific point in time.

The problem that explanatory models often are not identifiable from the data.

Models for relations between variables of continuous and discrete type based on conditional associations.

A network that represents within-person conditional associations between variables within the same time point. Contemporaneous networks are often estimated after conditioning on effects of the previous time point, as expressed in a time-series model.

A method to determine which edges of a mixed graphical model are to be included and excluded.

A social process that leads to higher prevalence of more extreme attitudes in a population, leading to a bimodal population distribution, with only strong supporters and opponents, rather than a normal distribution in which most people obtain a middle position.

A regularization parameter to determine edge inclusion/exclusion that obtains a nominal false positive rate.

The amount by which an estimate differs from the target value.

An algorithm to obtain a network in which each node, in turn, is used as the dependent variable in a penalized regression function to identify which other nodes are connected to the relevant node.

Approaches that do not use a penalized likelihood function in network structure estimation but rely on different methodologies for edge selection, such as null hypothesis testing or Bayesian approaches.

A concept that expresses the degree to which two nodes have the same position in the network topology. Two nodes with high topological overlap have very similar connections to other nodes.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Cite this article.

Borsboom, D., Deserno, M.K., Rhemtulla, M. et al. Network analysis of multivariate data in psychological science. Nat Rev Methods Primers 1 , 58 (2021). https://doi.org/10.1038/s43586-021-00055-w

Download citation

Accepted : 12 July 2021

Published : 19 August 2021

DOI : https://doi.org/10.1038/s43586-021-00055-w

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

This article is cited by

Differences in the depression and burnout networks between doctors and nurses: evidence from a network analysis.

• Zheng Zhang
• Jiansong Zhou

BMC Public Health (2024)

New psychometric evidence from the Revised Mental Health Inventory (R-MHI-5) in Peruvian adolescents from a network psychometrics approach

• Estefany Rojas-Mendoza
• Vaneryn Alania-Marin
• Aaron Travezaño-Cabrera

BMC Psychology (2024)

Network analysis of Tourette syndrome and attention-deficit/hyperactivity disorder symptoms in children and adolescents

• Wenyan Zhang
• Zhongliang Jiang
• Tianyuan Lei

Child and Adolescent Psychiatry and Mental Health (2024)

Pathways to experienced coercion during psychiatric admission: a network analysis

• Benedetta Silva
• Stéphane Morandi
• Philippe Golay

BMC Psychiatry (2024)

eHealth tools use and mental health: a cross-sectional network analysis in a representative sample

• Dominika Ochnik
• Marta Cholewa-Wiktor
• Magdalena Pataj

Scientific Reports (2024)

Quick links

• Explore articles by subject
• Guide to authors
• Editorial policies

Sign up for the Nature Briefing: AI and Robotics newsletter — what matters in AI and robotics research, free to your inbox weekly.

Social Network Analysis: A Survey on Process, Tools, and Application

New citation alert added.

This alert has been successfully added and will be sent to:

You will be notified whenever a record that you have chosen has been cited.

To manage your alert preferences, click on the button below.

New Citation Alert!

Please log in to your account

Information & Contributors

Bibliometrics & citations.

• Lee S Tanveer J Rahmani A Alinejad-Rokny H Khoshvaght P Zare G Malekpour Alamdari P Hosseinzadeh M (2025) SFGCN: Synergetic fusion-based graph convolutional networks approach for link prediction in social networks Information Fusion 10.1016/j.inffus.2024.102684 114 (102684) Online publication date: Feb-2025 https://doi.org/10.1016/j.inffus.2024.102684
• Kumar Meena S Sheshar Singh S Singh K (2024) Cuckoo Search Optimization-Based Influence Maximization in Dynamic Social Networks ACM Transactions on the Web 10.1145/3690644 Online publication date: 28-Aug-2024 https://dl.acm.org/doi/10.1145/3690644

Index Terms

Information systems

Information systems applications

Collaborative and social computing systems and tools

Social networking sites

World Wide Web

Online advertising

Social advertising

Web applications

Social networks

Recommendations

Social network analysis: a survey on measure, structure, language information analysis, privacy, and applications.

The rapid growth in popularity of online social networks provides new opportunities in computer science, sociology, math, information studies, biology, business, and more. Social network analysis (SNA) is a paramount technique supporting understanding ...

Broad Learning:: An Emerging Area in Social Network Analysis

Looking from a global perspective, the landscape of online social networks is highly fragmented. A large number of online social networks have appeared, which can provide users with various types of services. Generally, information available in these ...

Understanding user behavior in a local social media platform by social network analysis

Characterizing user behavior by social network analysis in social media has been an active research domain for a long time. However, much previous research has focused on the large-scale global social media such as Facebook, Wikipedia and Twitter. ...

Information

Published in.

Swiss Federal Institute of Technology Lausanne (EPFL), Switzerland

University of Bologna, Italy

Association for Computing Machinery

New York, NY, United States

Publication History

Check for updates, author tags.

• Information diffusion
• influence maximization
• link prediction
• community detection
• social network analysis

Contributors

Other metrics, bibliometrics, article metrics.

• 2 Total Citations View Citations
• 1,191 Total Downloads
• Downloads (Last 12 months) 1,191
• Downloads (Last 6 weeks) 169

View Options

Login options.

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

View options.

View or Download as a PDF file.

View online with eReader .

View this article in Full Text.

Share this Publication link

Copying failed.

Share on social media

Affiliations, export citations.

• Please download or close your previous search result export first before starting a new bulk export. Preview is not available. By clicking download, a status dialog will open to start the export process. The process may take a few minutes but once it finishes a file will be downloadable from your browser. You may continue to browse the DL while the export process is in progress. Download
• Download citation
• Copy citation

We are preparing your search results for download ...

We will inform you here when the file is ready.

Your file of search results citations is now ready.

Your search export query has expired. Please try again.

Our systems are now restored following recent technical disruption, and we’re working hard to catch up on publishing. We apologise for the inconvenience caused. Find out more: https://www.cambridge.org/universitypress/about-us/news-and-blogs/cambridge-university-press-publishing-update-following-technical-disruption

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings .

Login Alert

• > Journals
• > Studies in Second Language Acquisition
• > Volume 45 Issue 2
• > Network analysis for modeling complex systems in SLA...

Article contents

Introduction, research designs in cdst, expanding our research agenda, network analysis, network analysis and cdst, network estimation and visualization, supplementary materials, data availability statement, network analysis for modeling complex systems in sla research.

Published online by Cambridge University Press:  14 October 2022

• Supplementary materials

Network analysis is a method used to explore the structural relationships between people or organizations, and more recently between psychological constructs. Network analysis is a novel technique that can be used to model psychological constructs that influence language learning as complex systems, with longitudinal data, or cross-sectional data. The majority of complex dynamic systems theory (CDST) research in the field of second language acquisition (SLA) to date has been time-intensive, with a focus on analyzing intraindividual variation with dense longitudinal data collection. The question of how to model systems from a structural perspective using relation-intensive methods is an underexplored dimension of CDST research in applied linguistics. To expand our research agenda, we highlight the potential that psychological networks have for studying individual differences in language learning. We provide two empirical examples of network models using cross-sectional datasets that are publicly available online. We believe that this methodology can complement time-intensive approaches and that it has the potential to contribute to the development of new dimensions of CDST research in applied linguistics.

In the field of second language acquisition (SLA), complex dynamic systems theory (CDST) is a theoretical paradigm used to study the complex and dynamic nature of language, language use, and language development (Hulstijn, Reference Hulstijn 2020 ). A complex system is formed out of interactions between multiple internal and external system components. For example, if conceptualizing language development as a complex system, changes in development are dependent on interactions between a learner’s internal resources like working memory, motivation, and personality, as well as external, environmental resources like the teacher, learning materials, and language use (van Geert, Reference van Geert 1991 ). These internal and external resources are interrelated, whereby altering one component could in turn alter other components of the system (de Bot et al., Reference de Bot, Lowie and Verspoor 2007 ). In this way, a complex system is characterized by complete interconnectedness and mutual causality (Larsen-Freeman & Cameron, Reference Larsen-Freeman and Cameron 2008 ). Complex systems are inherently dynamic; systems emerge over time through processes of self-organization and coadaptation between micro- and macro-level system components (Larsen-Freeman, Reference Larsen-Freeman 1997 ). This means that complex systems are soft-assembled, whereby systems are “more than the sum of their parts, reflecting a multiplicative combination of attributes, experiences and situational factors” (American Psychological Association, 2017 ). CDST researchers in SLA have acknowledged the impossibility of fully “knowing” a system, as complex systems are characterized by unpredictability and nonlinearity, where changes in the system can be disproportionate to the cause (Larsen-Freeman, Reference Larsen-Freeman 1997 ). Although a complex system is, by definition, constantly in flux, the system can also demonstrate periods of temporary stability. This is referred to as an attractor state; a self-sustaining state in which interactions “are actively reproduced over time” (van Geert, Reference van Geert 2019 , p. 168). An attractor state represents higher-order patterns of self-organization within state space, from which the system moves toward or away from over time (Hiver, Reference Hiver, Dörnyei, MacIntyre and Henry 2014 ). To illustrate, an attractor state could refer to the tendency for learners not to participate in class and remain silent (Hiver, Reference Hiver, Dörnyei, MacIntyre and Henry 2014 ).

With the growing recognition that CDST approximates the reality of language development (Hiver & Al-Hoorie, Reference Hiver and Al-Hoorie 2020a ), more SLA researchers are adopting this framework. However, there are many methodological considerations for conducting empirical research within a CDST paradigm. Some of these include how to operationalize the system, how to assess the influence of contextual factors on the system, as well as macro- and micro-structure considerations (Hiver & Al-Hoorie, Reference Hiver and Al-Hoorie 2016 ). Given the inherent complexities of analyzing dynamic cause-effect relationships between systems and their components, there has been much discussion about suitable methodologies and suggestions of how to enhance our CDST toolbox (de Bot, Reference De Bot, Verspoor, de Bot and Lowie 2011 ; Hiver & Al-Hoorie, Reference Hiver and Al-Hoorie 2016 , Reference Hiver and Al-Hoorie 2020a ; Hiver et al., Reference Hiver, Al-Hoorie and Evans 2022 ).

Hilpert and Marchand ( Reference Hilpert and Marchand 2018 ) distinguish between three conceptual perspectives to studying complex systems and their accompanying research designs: time-intensive, relation-intensive, and time-relation intensive approaches. Firstly, time-intensive approaches “are used to make inferences about system behavior using closely spaced observations over time” using longitudinal data (Hilpert & Marchand, Reference Hilpert and Marchand 2018 , p. 192). The second approach, relation-intensive, focuses on identifying the structure of the relationships among individuals or variables in a system using cross-sectional data. Combining the first two approaches, time-relation intensive approaches “are used to make inferences about system behavior using closely spaced, simultaneously collected observations of both within-element change and changing between element relationships” (Hilpert & Marchand, Reference Hilpert and Marchand 2018 ).

The majority of CDST studies in the field of SLA to date have taken time-intensive approaches, typically consisting of case studies characterized by dense data collection with qualitative and descriptive data analyses (Hiver et al., Reference Hiver, Al-Hoorie and Evans 2022 ). For the last 30 years, CDST researchers have focused on individual variability and the dynamics of processes (van Geert & van Dijk, Reference van Geert and van Dijk 2021 ). This is not surprising, given that CDST is essentially a theory of change, concerned with how one state develops into another state over time. However, as Hilpert and Marchand ( Reference Hilpert and Marchand 2018 ) have pointed out, complex systems can be studied from multiple perspectives. Besides analyzing change over time, identifying the structure of a system is also a key aspect of CDST. Expanding our line of inquiry to include relation-intensive approaches could contribute to the development of new dimensions of CDST research and complement time-intensive approaches. While researchers have a diverse selection of methods available for time-intensive approaches, our methodological toolbox for relation-intensive methods is lacking.

In this article, we highlight network analysis as a potential methodology to model complex systems from a relation-intensive perspective. While network analysis can also be used for time- and time-relation intensive approaches, this article is focused on network analysis for relation-intensive approaches only, due to the relative lack of attention that this dimension has received by SLA researchers working within a CDST paradigm. More specifically, we concentrate on psychological networks , as opposed to social networks. SLA researchers have already explored social network analysis as a suitable research methodology for CDST, for example to model relationships between learners in a classroom and teacher networks as complex systems (Hiver & Al-Hoorie, Reference Hiver and Al-Hoorie 2016 ; Hiver & Al-Hoorie, Reference Hiver and Al-Hoorie 2020a ; Mercer, Reference Mercer, Dörnyei, MacIntyre and Henry 2014 ). SLA researchers have not yet explored the potential of psychological networks to model psychological constructs that influence language learning as complex systems. The network approach to psychopathology has been used to reevaluate theories of mental disorders (Borsboom et al., Reference Borsboom, Fried, Epskamp, Waldorp, van Borkulo, van der Maas and Cramer 2017 ; Borsboom & Cramer, Reference Borsboom and Cramer 2013 ) and constructs such as intelligence and cognitive development from a CDST perspective (Kievit, Reference Kievit 2020 ; van der Maas et al., Reference van der Maas, Dolan, Grasman, Wicherts, Huizenga and Raijmakers 2006 , Reference van der Maas, Kan, Marsman and Stevenson 2017 ). In this article we discuss how, similarly to psychology research, individual differences in language learning can be modeled as nomological networks, expanding our relation-intensive methods to include the study of phenomenological constructs. We begin with a brief review of CDST research designs used in the field of SLA to date, in relation to the three different conceptual approaches to studying complex systems as described by Hilpert and Marchand ( Reference Hilpert and Marchand 2018 ). We then expand discussion on relation-intensive approaches, the least researched dimension in CDST. The remainder of the article discusses potential applications of network analysis. To further aid discussion, we provide two examples of network models that are estimated from publicly available data.

Time-intensive methods

Most CDST research in applied linguistics is time-intensive, with longitudinal data collection of a single variable (or multiple variables for a single case/participant) to observe micro-level changes in the system over time (Hiver et al., Reference Hiver, Al-Hoorie and Evans 2022 ; Hiver & Larsen-Freeman, Reference Hiver, Larsen-Freeman, Al-Hoorie and MacIntyre 2019 ). Time-intensive studies tend to have dense data collection and small sample sizes, with 40% of studies including a sample size of 10 participants or fewer (Hiver et al., Reference Hiver, Al-Hoorie and Evans 2022 ). A particularly researched area is the development of L2 writing over time using measures of complexity, fluency, and accuracy (CAF) (Evans & Larsen-Freeman, Reference Evans and Larsen-Freeman 2020 ; Larsen-Freeman, Reference Larsen-Freeman 2006 ; Lowie et al., Reference Lowie, van Dijk, Chan and Verspoor 2017 ; Lowie & Verspoor, Reference Lowie and Verspoor 2019 ). Some common CDST techniques used in these studies include assessing the degree of variability in developmental trajectories and plotting longitudinal data on min-max graphs for visual inspection. Several studies have used a time-series design based on the view that frequent-enough measurements may be able to capture underlying developmental processes (Van Geert & Steenbeek, Reference van Geert and Steenbeek 2005 ). For example, Waninge et al. ( Reference Waninge, Dörnyei and de Bot 2014 ) micro-mapped the motivational dynamics of four students during class time, taking measurements at 5-minute intervals.

Another popular methodology for observing language development is retrodictive modeling (Chan & Zhang, Reference Chang and Zhang 2021 ; Evans & Larsen-Freeman, Reference Evans and Larsen-Freeman 2020 ; Nitta & Baba, Reference Nitta, Baba and Bygate 2018 ), based on the idea that because what we observe has already changed, change can be described retrospectively (Larsen-Freeman & Cameron, Reference Larsen-Freeman and Cameron 2008 ). Retrodictive methods such as process tracing have been used to study the development of language as well as individual differences over time. For example, Papi and Hiver ( Reference Papi and Hiver 2020 ) used process tracing of retrospective interviews to examine changes in six learners’ motivational principles and Amerstorfer ( Reference Amerstorfer 2020 ) used process tracing with a combination of classroom observations and retrodictive interviews to explore five learners’ strategic L2 development. Some time-intensive CDST studies have also used the “idiodynamic method,” a mixed-methods approach to studying affective and cognitive states (MacIntyre, Reference MacIntyre 2012 ). These time-intensive approaches have provided insights into nonlinear L2 developmental processes and intraindividual variation over time.

Relation-intensive methods

In comparison to the number of studies that have taken a time-intensive approach, far fewer CDST studies have taken a relation-intensive approach, which involves exploring the structure of relationships between people or variables within a system with cross-sectional data. As previously mentioned, SLA researchers have noted how social network analysis is a suitable methodology for CDST, for example to analyze relationships between learners in a classroom, teacher networks, or school networks (Mercer, Reference Mercer, Dörnyei, MacIntyre and Henry 2014 ). However, this discussion has been mostly theoretical, with very few empirical studies using social network analysis from a CDST perspective. For example, although some applied linguistics researchers have used social network analysis to map the distribution of conversational topics of bilinguals in different contexts (Tiv et al., Reference Tiv, Gullifer, Feng and Titone 2020 ) and to assess the impact of social networks in study abroad contexts (Gautier, Reference Gautier and Howard 2019 ; Paradowski et al., Reference Paradowski, Jarynowski, Jelińska and Czopek 2021 ; Zappa-Hollman & Duff, Reference Zappa-Hollman and Duff 2014 ), these studies are not typically informed by CDST.

While relation-intensive approaches can focus on person-to-person interactions, they can also be used to analyze relations among psychological variables (Marchand & Hilpert, Reference Marchand and Hilpert 2018 ). Taking a variable-centered relation-intensive approach necessitates researchers to engage with psychological constructs on a phenomenological level, and to carefully consider whether their methodology can effectively model complex patterns of relationships among variables. Some SLA researchers have discussed how psychological constructs such as “the self” and L2 motivation can be conceptualized as complex systems (Henry, Reference Henry, Dörnyei, MacIntyre and Henry 2014 , Reference Henry 2017 ; Mercer, Reference Mercer 2011a ). In one study, Mercer ( Reference Mercer 2011a ) took a relation-intensive approach to explore how the self-construct could be conceived of as a complex system. Using qualitative data of a single case study, Mercer ( Reference Mercer 2011a ) created a three-dimensional network-based model of a student’s self-concepts that she felt to be the most “phenomenologically-real” representation of the data.

Besides this, few SLA researchers have attempted to model psychological constructs as complex systems. There are a handful of CDST studies that are reminiscent of relation-intensive approaches, which used quantitative methodologies often deemed ill-suited for CDST. For example, conceptualizing L2 speech as a complex system, Saito et al. ( Reference Saito, Macmillan, Mai, Suzukida, Sun, Magne, Ilkan and Murakami 2020 ) investigated the effects that 30 different internal and external individual differences had on the pronunciation of 110 L2 English speakers. Due to the large number of variables included in their study, Saito et al. ( Reference Saito, Macmillan, Mai, Suzukida, Sun, Magne, Ilkan and Murakami 2020 ) first conducted factor analysis and then did regression analysis with the extracted factor scores on speech ratings. In another study, Li et al. ( Reference Li, Dewaele and Jiang 2020 ) positioned themselves within a CDST framework to explore the relationships between individual difference constructs including foreign language classroom anxiety, foreign language enjoyment, self-perceived achievement, and actual English achievement. To analyze data, Li et al. ( Reference Li, Dewaele and Jiang 2020 ) conducted Pearson correlations to assess relationships between variables and used multiple regression analysis to assess the combined effect of anxiety and enjoyment on language achievement. While these two studies are fine cross-sectional studies in their own right, CDST scholars have argued that methods such as zero-order correlations and linear regression oversimplify the complex realities of how individual differences influence second language development and have questioned the use of cross-sectional datasets in CDST research (Al-Hoorie & Hiver, Reference Al-Hoorie, Hiver, Al-Hoorie and Szabó 2022 ; Hiver, Reference Hiver, Dörnyei, MacIntyre and Henry 2014 ). Overall, very few SLA researchers to date have used relation-intensive approaches within a CDST paradigm. There are also seemingly fewer methodologies available for SLA researchers to explore relation-intensive approaches, with more conceptual discussion than empirical studies.

Time-relation intensive methods

Hilpert and Marchand ( Reference Hilpert and Marchand 2018 , p. 192) describe time-relation intensive research designs as having “closely spaced, simultaneously collected observations of both within-element change and changing between element relationships.” Only a few SLA studies have analyzed interactions between variables and how these interactions change over time. However, these studies cannot be strictly classified as time-relation intensive approaches, as their data collection consisted of only a few time points. For example, Serafini ( Reference Serafini 2017 ) conducted longitudinal case studies to explore interactions between cognitive and motivational individual differences at varying proficiency levels. Data was collected twice from 87 university students learning L2 Spanish, at the beginning and end of an academic semester. Serafini used Pearson correlations to analyze associations between individual differences at each time point and created scatterplots with regression and Loess lines to visualize relationships between variables and compare differences across proficiency levels. Results showed that the relationship between cognitive abilities and motivational constructs varied at each time point and across learner proficiency levels, indicating that cognitive and motivational subsystems are interdependent. In another study, Piniel and Csizér ( Reference Piniel, Csizér, Dörnyei, MacIntyre and Henry 2014 ) investigated changes in 21 students’ motivation, anxiety, and self-efficacy at six time points throughout an academic writing course. To analyze data, Piniel and Csizér used latent growth curve modeling (LGCM) and cluster analysis to group together learners with similar trajectories. Interactions between variables were also analyzed by comparing Pearson correlations between IDs at each time point. Overall, results indicated that language learning experience, ought-to L2 self, and writing anxiety showed a significant level of nonlinear change over time. There was also a strong interrelationship between motivation and anxiety, whereby more highly motivated learners had lower levels of language learning anxiety.

Pfenninger and colleagues (Kleisch & Pfenninger, Reference Kliesch and Pfenninger 2021 ; Pfenninger, Reference Pfenninger 2020 ) have also recently explored the use of generalized additive mixed modeling (GAMM) for a time-relation intensive approach to SLA microdevelopment. GAMM is a type of analysis used for time-series data that can consider nonlinear development, iterative processes, and interdependency between variables (Pfenninger, Reference Pfenninger 2020 ). Pfenninger ( Reference Pfenninger 2020 ) used GAMM to analyze the L2 developmental trajectories of four groups of children (N = 91) on different content and language integrated learning (CLIL) programs. The children completed various language tasks four times a year for up to 8 years. Pfenninger also combined GAMM with qualitative data to help identify what contributed to developmental trajectories. Results showed that children had similar L2 trajectories regardless of their age of onset, and that L2 growth was determined by various different external and internal states across time. In another study, Kliesch and Pfenninger ( Reference Kliesch and Pfenninger 2021 ) used GAMM to examine the L2 developmental trajectories of 28 adults (age 64+) on a 7-month beginner’s Spanish course. Data was collected each week over 30–32 weeks, which included seven L2 measures, eight cognitive tasks, and measures of well-being and motivation. GAMM revealed both linear and nonlinear increases in L2 proficiency over time, with considerable between-subject variability. While only a few CDST studies have used time-relation intensive methods, findings indicate a complex interplay between external and internal learner differences, which in turn interact with language development in a nonlinear way over time.

CDST studies that have incorporated a relation-intensive element to their research design are far less common compared to the number of studies that have taken time-intensive approaches. Despite the fact that “complexity theorists are interested in understanding the relations [emphasis in original] that connect the components of a complex system” (Hiver & Larsen-Freeman, Reference Hiver, Larsen-Freeman, Al-Hoorie and MacIntyre 2019 , p. 287), to date there have been very few attempts to empirically model these relations. One potential reason behind this is relates to methodological challenges and the view that cross-sectional data, zero-order correlations and linear regression are ill-suited to studying complex systems (Al-Hoorie & Hiver, Reference Al-Hoorie, Hiver, Al-Hoorie and Szabó 2022 ). Another reason relates to the theoretical challenges of conceptualizing abstract psychological constructs as complex systems. A number of individual differences constructs in language learning have been conceptualized as complex systems, such as motivation (Papi & Hiver, Reference Papi and Hiver 2020 ), strategy development (Amerstorfer, Reference Amerstorfer 2020 ), anxiety (Gregersen, Reference Gregersen 2020 ), working memory (Jackson, Reference Jackson 2020 ), and willingness to communicate (MacIntyre, Reference MacIntyre 2020 ). To examine these constructs from a relation-intensive perspective, for example to model L2 motivation as a complex system, we must consider the components that form the system, and how these components align with our measurement instruments. Researchers must also confront “the boundary problem” (Larsen-Freeman, Reference Larsen-Freeman, Ortega and Han 2017 ), accepting the theoretical impossibility of measuring a complex system in its entirety, whereby “the whole is greater than the sum of its parts” (Han, Reference Han and Han 2019 , p. 156). Consideration should also be given to the phenomenological validity of equating conceptual and theoretical concepts as systems, and the practical implications this has for a chosen methodology (Hiver & Al-Hoorie, Reference Hiver and Al-Hoorie 2016 ). Mercer ( Reference Mercer and Mercer 2011b , p. 59) discusses these issues in relation her network-based model of the self-concept, acknowledging the theoretical and empirical difficulty of distinguishing the blurred boundaries between different self-constructs. Despite the challenges of exploring psychological constructs related to language learning from a relation-intensive approach, and the inevitable reductionism this entails, focusing on system structures can offer a perspective that is currently missing from CDST research in SLA.

Take the construct of L2 motivation, for example, which has been much discussed in CDST research (e.g., Dörnyei, Reference Dörnyei, Ortega and Han 2017 , Dörnyei et al., Reference Dörnyei, MacIntyre, Henry, Dörnyei, MacIntyre and Henry 2015 ; Henry, Reference Henry, Dörnyei, MacIntyre and Henry 2014 , Reference Henry 2017 ; Hiver & Papi, Reference Hiver, Papi, Lamb, Csizér, Henry and Ryan 2019 ; Hiver & Larsen-Freeman, Reference Hiver, Larsen-Freeman, Al-Hoorie and MacIntyre 2019 ; Papi & Hiver, Reference Papi and Hiver 2020 ). Most CDST research on L2 motivation has been time-intensive with a focus on observing micro-level changes in a small number of variables over time. Very few CDST researchers have explored L2 motivation from a relation-intensive perspective, although there has been some theoretical discussion of how to conceptualize the structural relationships between motivational constructs as complex systems (Henry, Reference Henry, Dörnyei, MacIntyre and Henry 2014 , Reference Henry 2017 ). The L2 Motivational Self System (L2MSS) is a theoretical paradigm that was developed by Dörnyei ( Reference Dörnyei 2005 , Reference Dörnyei, Ellis and Larsen-Freeman 2009 ) that conceptualizes L2 motivation from a self-perspective. The L2MSS is comprised of three phenomenologically constructed concepts, each theorized to be a primary source of motivation to learn an L2: the Ideal L2 Self, the Ought-to L2 Self, and L2 Learning Experience (Dörnyei Reference Dörnyei 2005 , Reference Dörnyei, Ellis and Larsen-Freeman 2009 ). Although the L2MSS was not originally conceptualized as a complex system, it has been conceptually extended to a CDST paradigm (Henry, Reference Henry, Dörnyei, MacIntyre and Henry 2014 , Reference Henry 2017 ). For example, Henry ( Reference Henry 2017 , p. 551) has described the self-concept as a multifaced dynamic structure, which can be understood as “the product of constant interactions between different subsystems (such as, e.g., self-efficacy and self-esteem).”

Taking a relation-intensive approach to L2 motivation could provide insight into the structural relationships between components of the L2 motivational system, and if this were expanded to a time-relation intensive approach, could potentially identify attractor states. SLA researchers have speculated about how the L2 self-system, in particular the Ideal L2 self, can manifest as an attractor state (Henry, Reference Henry 2017 ; Hiver, Reference Hiver, Dörnyei, MacIntyre and Henry 2014 ; Waninge et al., Reference Waninge, Dörnyei and de Bot 2014 ), whereby “changes in the vision of the Ideal L2 Self and changes in the distance between it and the actual self, can be conceptualized as changes in attractor state geometries ” (Henry, Reference Henry, Dörnyei, MacIntyre and Henry 2014 , p. 87, emphasis in original). Although longitudinal data is needed to show system self-organization and the emergence of attractor states, cross-sectional data can provide a perspective that is currently missing from CDST research in SLA. As Mercer ( Reference Mercer 2011a ) reflects in relation to her network-based model of the self-concept:

Whilst the model out of necessity can only represent a snapshot of a fragment of an individual’s self-concept network in a specific context at a particular time, the essence of the underlying form can be used to fundamentally understand the structure and nature of self-concept. (p. 66)

Taking a relation-intensive CDST approach to the study of individual differences in SLA can thus be viewed as complimentary of time-intensive approaches. Cross-sectional data can provide insight into the structure of relationships between system components, which, if combined with what we have learned from time-intensive CDST studies, could enrich our understanding of the complex interplay between individual differences and L2 development.

There is currently little guidance on how to analyze and model interactions between system components from a relation-intensive perspective. As previously mentioned, CDST researchers have questioned whether methods such as zero-order correlations and linear regression are suitable for examining dynamic changes and interconnected (Al-Hoorie & Hiver, Reference Al-Hoorie, Hiver, Al-Hoorie and Szabó 2022 ). Although scholars have emphasized the potential of quantitative analyses for CDST research (Al-Hoorie & Hiver, Reference Al-Hoorie, Hiver, Al-Hoorie and Szabó 2022 ) for example to identify network structure or nested phenomena, there appears to be an overall reluctance to use cross-sectional data, with most CDST researchers preferring longitudinal data. Until now, most studies that have taken a relation-intensive approach have analyzed relationships between variables by correlations and multiple regression analysis (Li et al., Reference Li, Dewaele and Jiang 2020 ; Piniel & Csizér, Reference Piniel, Csizér, Dörnyei, MacIntyre and Henry 2014 ; Saito et al., Reference Saito, Macmillan, Mai, Suzukida, Sun, Magne, Ilkan and Murakami 2020 ; Serafini, Reference Serafini 2017 ). However, new advancements in statistics software and data analysis techniques such as GAMM are enriching the CDST toolbox. Other techniques that have been proposed as appropriate methods to study complex systems with a relation-intensive element are latent growth curve modeling (LGCM) and multilevel modeling (MLM) (Hiver & Al-Hoorie, Reference Hiver and Al-Hoorie 2020a ; MacIntyre et al., Reference MacIntyre, MacKay, Ross, Abel, Ortega and Han 2017 ). To expand our CDST toolbox of relation-intensive approaches, we could also utilize network analysis, an underexplored methodology in SLA research.

Network analysis has become a popular technique for studying complex systems in the field of psychology. Readers should be aware that there are many different types of network models; network analysis can be performed on cross-sectional data from a relation-intensive perspective (Epskamp & Fried, Reference Epskamp and Fried 2019 ; Hevey, Reference Hevey 2018 ), and also on longitudinal time-series data from a time- or time-relation intensive perspective (Bringmann et al., Reference Bringmann, Vissers, Wichers, Geschwind, Kuppens, Peeters and Tuerlinckx 2013 ). Although we outline some other variants of network analysis later in the discussion section, it is beyond the scope of this article to describe each type of network analysis in detail. We have opted to focus on psychological networks with cross-sectional data for relation-intensive approaches, which is an underexplored dimension of CDST research in applied linguistics.

As readers may be more familiar with social network analysis, we would also like to briefly explain some differences between social networks and psychological networks. Social networks show patterns of relationships among individuals or groups, whereas psychological networks show patterns of relationships among variables (at item level or composite level). It is important to note that with social networks, the relationships between variables are known ; social networks are created from an adjacency matrix, whereby the relationships between variables are directly observed (O’Malley & Onnela, Reference O’Malley, Onella, Levy, Goring, Gatsonis, Sobolev, van Ginneken and Busse 2019 ). In contrast, with psychological networks, relationships between variables are not known but are estimated. Psychological networks are estimated from a variance-covariance matrix, based on the strength of partial correlations between variables (Epskamp & Fried, Reference Epskamp and Fried 2019 ).

Psychological network analysis has been used to model constructs such as intelligence (van der Maas et al., Reference van der Maas, Dolan, Grasman, Wicherts, Huizenga and Raijmakers 2006 , Reference van der Maas, Kan, Marsman and Stevenson 2017 ) cognitive development (Kievit, Reference Kievit 2020 ), and mental disorders (Borsboom, Reference Borsboom, Fried, Epskamp, Waldorp, van Borkulo, van der Maas and Cramer 2017 ) from a CDST perspective, and has also been applied to clinical research on psychological disorders such as depression and eating disorders (Elliott et al., Reference Elliott, Jones and Schmidt 2020 ; Lutz et al., Reference Lutz, Schwartz, Hofmann, Fisher, Husen and Rubel 2018 ). In network models, variables (also referred to as components) are represented as circles called nodes. In psychological networks, nodes represent elements of a construct or an entire construct, such as attitudes or symptoms of a mental disorder. Lines between nodes are called edges , which represent the direct association between a pair of nodes. The strength of association between nodes is called the edge weight ; the thicker the edge, the stronger the association. Edges in psychological networks are typically undirected , which reflect the hypothesized multicausal relationships between system components. Positive relationships are typically denoted using blue edges, while red edges are used to indicate negative relationships. The layout of the network model can be selected by the researcher. Psychological networks are often plotted (by default) using the Fruchterman-Reingold algorithm (Fruchterman & Reingold, Reference Fruchterman and Reingold 1991 ), which places nodes with stronger connections closer together, and nodes with weaker connections further apart. Besides visual inspection, network models can be analyzed on several different levels, depending on what the research questions are. For example, researchers typically analyze the network density if the overall interest is the network structure or focus on particular nodes and edges (Burger et al., Reference Burger, Isvoranu, Lunansky, Haslbeck, Epskamp, Hoekstra, Fried, Borsboom and Blanken 2022 ).

The most common models used to estimate psychological networks are pairwise Markov random field (PMRF) models. Within PRMF models, Gaussian graphical models (GGM) are used with continuous multivariate data to estimate partial correlations between variables (Epskamp, Reference Epskamp 2014 ). Partial correlation networks are undirected graphs, estimated by analyzing the strength of correlations between variables after controlling for the effect of other measured variables in the network (Hevey, Reference Hevey 2018 ). As such, a psychological network can be viewed as a “nomological net, which functions as a specification of the phenomenological concepts or theoretical constructs of interest in a study, their observable manifestations, and the linkages between them” (Hiver & Al-Hoorie, Reference Hiver and Al-Hoorie 2016 , p. 747). Psychological networks created using cross-sectional data can therefore be viewed as a snapshot of the system at a given time.

Network analysis has some advantages over other relation-intensive methods used in CDST research. One advantage is that network analysis is more conceptually aligned with CDST compared to factor-based statistical techniques that are rooted in latent variable theory (Fried, Reference Fried 2020 ). Originally developed by Spearman ( Reference Spearman 1904 ), factor models function under the theoretical assumption that a latent construct, such as intelligence or personality, can be measured through observable indicators (e.g., behavioral tests or questionnaire items). This means that there is a hypothesized unidirectional relationship from the latent construct to the observable indicator, whereby answers to questionnaire items or tests are thought to “reflect” the latent construct (Edward & Bagozzi, Reference Edwards and Bagozzi 2000 ). In contrast, from a network perspective, psychological constructs “exist as systems where components mutually influence each other without the need to call on latent variables” (Guyon et al., Reference Guyon, Falissard and Kop 2017 , p. 2). Statistically, factor models and psychological networks are closely related, as both analyze the covariance between observed variables. The difference between each approach is their competing causal explanations (Fried, Reference Fried 2020 ). As van Bork et al. ( Reference van Bork, Rhemtulla, Waldorp, Kruis, Rezvanifar and Borsboom 2019 , p. 1) explain, “whereas latent variable approaches introduce unobserved common causes to explain the relations among observed variables, network approaches posit direct causal relations between observed variables.”

These two competing causal explanations are reflected in the choice of statistical model selected by the researcher. For example, factor-based techniques such as SEM or LGCM generate directed graphs, with edges from the latent construct to the observed indicators and/or between latent constructs, which are determined by the researcher a priori. Psychological network analysis is a more data-driven approach and produces an undirected graph with edges estimated between all nodes, better reflecting key CDST concepts such as multicausality and interconnectedness. This has already been noted in the field of psychology, where researchers working from a CDST perspective are using network analysis as an exploratory tool to better visualize the complex patterns of relations between variables of interest (Hilpert & Marchand, Reference Hilpert and Marchand 2018 ; Sachisthal et al., Reference Sachisthal, Jansen, Peetsma, Dalege, van der Maas and Raijmakers 2019 ; van der Maas et al., Reference van der Maas, Kan, Marsman and Stevenson 2017 ).

In this article, we explore how network analysis could be used to model psychological constructs that influence language learning from a relation-intensive perspective. We provide two examples of psychological networks created using the datasets of existing studies that are publicly available online in support of Open Science practices. As the nested nature of educational phenomena can be analyzed at multiple levels (Marchand & Hilpert, Reference Marchand and Hilpert 2018 ), our network models illustrate two different levels of analysis; with nodes at item level and composite level. The first example is a network model of L2 motivation made using the dataset from Hiver and Al-Hoorie’s ( Reference Hiver and Al-Hoorie 2020b ) study on the role of vision in L2 motivation. This example explores how an individual difference construct such as L2 motivation can be modeled as a complex system, by analyzing relationships between the L2MSS at the item level. The second example is a network model of individual differences in native language ultimate attainment, made using the dataset from Dąbrowska’s ( Reference Dąbrowska 2018 ) study. The second example takes a wider relation-intensive perspective by analyzing interactions between multiple individual difference constructs at the composite level. Note that the authors of the original studies (Dąbrowska, Reference Dąbrowska 2018 ; Hiver & Al-Hoorie, Reference Hiver and Al-Hoorie 2020b ) did not position their research within a CDST paradigm, and our reanalysis of their data is not a critique on their work.

We performed all statistical analyses using the open-source software R (R Core Team, 2020 ) and the R-packages qgraph (Epskamp et al., Reference Epskamp, Cramer, Waldorp, Schmittmann and Borsboom 2012 ) and bootnet (Epskamp et al., Reference Epskamp, Borsboom and Fried 2018a ) in particular. The R code that we used to create these two examples is available in the online Supplementary Materials on our Open Science Framework (OSF) page. This article is not intended to serve as a tutorial in network analysis (for tutorials, we refer readers to Burger et al., Reference Burger, Isvoranu, Lunansky, Haslbeck, Epskamp, Hoekstra, Fried, Borsboom and Blanken 2022 ; Epskamp et al., Reference Epskamp, Borsboom and Fried 2018a ; and Hevey, Reference Hevey 2018 ). Rather, our overall aim is to raise awareness of this methodology and illustrate how it can be applied to model psychological constructs related to language learning from a relation-intensive CDST perspective. Within each example, we evaluate (a) the extent to which a network analysis of the datasets supports the same conclusions as the original authors and (b) whether network analysis can offer any additional insights to the original analyses.

The first example was made using the dataset from Hiver and Al-Hoorie’s ( Reference Hiver and Al-Hoorie 2020b ) study “Reexamining the Role of Cision in Second Language Motivation: A Preregistered Conceptual Replication of You, Dörnyei, and Csizér ( Reference You, Dörnyei and Csizér 2016 ).” Both Hiver and Al-Hoorie ( Reference Hiver and Al-Hoorie 2020b ) and You et al. ( Reference You, Dörnyei and Csizér 2016 ) used SEM to explore interrelationships between components of the L2 Motivational Self System (L2MSS). The L2MSS is a theoretical paradigm that was developed by Dörnyei ( Reference Dörnyei 2005 , Reference Dörnyei, Ellis and Larsen-Freeman 2009 ) based on Possible Selves Theory (Markus & Nurius, Reference Markus and Nurius 1986 ). The L2MSS is comprised of three components, each theorized to be a primary source of motivation to learn an L2: the Ideal L2 Self, the Ought-to L2 Self, and L2 Learning Experience. The ideal L2 self refers to learners’ internal desires and wishes to learn the L2, while the ought-to L2 self refers to learner’s perceived external duties and social pressures to learn the L2 (Dörnyei & Chan, Reference Dörnyei and Chan 2013 ). L2 experience concerns learners’ attitudes toward learning, based on their experience of the learning process and environment. In addition to these three components, vision and imagery are also considered key aspects of the L2MSS, whereby motivation is viewed as “a function of the language learners’ vision of their desired future language selves” (Dörnyei & Chan, Reference Dörnyei and Chan 2013 , p. 437). Vision can be considered as a combination of imagery capacity and ideal selves and is typically measured by visual and auditory learning style preferences, and vividness of imagery capacity (You et al., Reference You, Dörnyei and Csizér 2016 ). A number of studies have used SEM to explore the interrelationships between these motivational constructs and the extent to which the L2MSS can predict language learning or intended effort (Dörnyei & Chan, Reference Dörnyei and Chan 2013 ; Hiver & Al-Hoorie, Reference Hiver and Al-Hoorie 2020b ; You et al., Reference You, Dörnyei and Csizér 2016 ). However, as You et al. ( Reference You, Dörnyei and Csizér 2016 , p. 97) have pointed out, “because the L2 Motivational Self System was originally proposed as a framework with no directional links among the three components, past empirical studies employing SEM have not been uniform in specifying these interrelationships.” For example, whereas some studies have presented a directed pathway from the ideal L2 self to L2 learning experience, other studies have reversed this relationship (for further details see You et al., Reference You, Dörnyei and Csizér 2016 ).

Hiver and Al-Hoorie ( Reference Hiver and Al-Hoorie 2020b ) conducted a conceptual replication and extension of You et al. ( Reference You, Dörnyei and Csizér 2016 ) to evaluate the role of vision in L2 motivation and to assess whether intended effort is an outcome or a predictor of motivation. They justified these aims in part due to the fact that You et al. did not test equivalent or competing models, which could be considered a form of confirmation bias. Hiver and Al-Hoorie also stressed the need for more robust research designs, and further replication of research on language motivation. Hiver and Al-Hoorie ( Reference Hiver and Al-Hoorie 2020b ) collected data from 1297 L2 learners of English in secondary schools in South Korea. In addition to the same 10 scales of motivation and vision used by You et al., Hiver and Al-Hoorie also included two measures of L2 proficiency, midterm grades and final exam grades, which were analyzed as one variable called L2 achievement. To determine the number of underlying factors, they submitted the dataset to Mokken scaling analysis, confirmatory factor analysis, exploratory factor analysis, scree plot, optimal coordinates, and parallel analysis (Hiver & Al-Hoorie, Reference Hiver and Al-Hoorie 2020b , p. 73). These analyses resulted in only four factors: visual style, ideal L2 self, ought-to L2 self, and intended effort. With these four factors and the measures of L2 achievement, Hiver and Al-Hoorie used SEM to test two competing causal models of vision and L2 motivation, where intended effort was either an antecedent or an outcome of motivation. Contrary to You et al. ( Reference You, Dörnyei and Csizér 2016 ), Hiver and Al-Hoorie hypothesized intended effort to be an antecedent of the ideal L2 self and the ought-to L2 self. In both competing models, vision (visual style) was considered a predictor of motivation, which was the same as You et al. ( Reference You, Dörnyei and Csizér 2016 ). Results showed that the model with intended effort as a predictor of motivation showed a better overall fit. Although this was contrary to You et al.’s model, Hiver and Al-Hoorie note that as their dataset and analyses differed greatly from the initial study, their model cannot be used to contradict You et al.’s model and call for further replication of research on the L2MSS.

In both studies (Hiver & Al-Hoorie, Reference Hiver and Al-Hoorie 2020b ; You et al., Reference You, Dörnyei and Csizér 2016 ), the authors were interested in the relationships between the L2MSS, vision, and intended effort. By using SEM, they operationalized motivational constructs as latent variables, depicting hypothesized causal relationships between latent constructs with unidirectional arrows. However, in both studies, the authors note potential issues and limitations of using SEM to model interactions between motivational constructs. One issue relates to the theorized dynamic nature of the L2MSS and the multicausal relationships between motivational constructs. Possible Selves Theory was originally proposed to have dynamic qualities, whereby current and ideal selves are shaped by multiple ongoing processes (Henry, Reference Henry, Dörnyei, MacIntyre and Henry 2014 ; Markus & Nurius, Reference Markus and Nurius 1986 ). For example, Hiver and Al-Hoorie speculate that once an L2 learner puts in the effort and engages in the L2 learning process, “there will be a dynamic interaction between motivation … and task demands, leading to continuous recalibration of that motivational construct” ( Reference Hiver and Al-Hoorie 2020b , p. 86). One might question the extent to which SEM can effectively model these dynamic interactions, as SEM operationalizes motivational constructs as latent variables with a unidirectional causal relationship. In fact, both studies’ authors acknowledge that a further limitation of SEM is that it requires the researcher to specify the direction of the relationship between latent constructs. SEM can only test the theoretical model that is selected by the researcher, although equivalent or alternative models may likely exist. This issue was illustrated by Hiver and Al-Hoorie’s ( Reference Hiver and Al-Hoorie 2020b ) two competing SEM models. As discussed earlier, there has already been discussion of how the L2MSS could be conceptualized as a complex system (Henry, Reference Henry, Dörnyei, MacIntyre and Henry 2014 , Reference Henry 2017 ) and manifest as an attractor state (Henry, Reference Henry 2017 ; Hiver, Reference Hiver, Dörnyei, MacIntyre and Henry 2014 ; Waninge et al., Reference Waninge, Dörnyei and de Bot 2014 ). From a CDST perspective, causal relationships between motivational constructs are not unidirectional, but reciprocal. To further investigate the relationship between motivation and intended effort, Hiver and Al-Hoorie ( Reference Hiver and Al-Hoorie 2020b ) have encouraged researchers to consider using nonrecursive models where causality is reciprocal. In this first example, we illustrate how network analysis can be used to model the L2MSS as a complex system, with hypothesized reciprocal causation between motivational constructs with nodes at item level.

Figure 1 is a GGM of the L2MSS that we made with the dataset from Hiver and Al-Hoorie’s ( Reference Hiver and Al-Hoorie 2020b ) study. In support of open science practices, they made their dataset and analyses publicly available through the OSF website. To allow for ease of comparison, we included the same variables in our network analysis as Hiver and Al-Hoorie’s SEM analyses, with the exception of visual style 2, which we explain in a later section. The network model in Figure 1 has nodes at item level, to better explore the interrelatedness of these motivational constructs, and the questionnaire items used to measure them. Table 1 contains information about which items correspond to each node.

Figure 1. A network model of the L2MSS and L2 achievement.

Note : In this network model of the L2MSS, there are four motivational constructs: the ideal L2 self, the ought-to L2 self, intended effort, and visual style. Each node represents a questionnaire item. Ought-to L2 self has been measured with six questionnaire items, and the other motivational constructs with five questionnaire items. There are also two composite measures of L2 proficiency: L2_T1 (students’ mid-term grades) and L2_T2 (students’ final grades).

Table 1. Legend of node labels

We chose GGM model selection (ggmModSelect function implemented in the bootnet R-package; Epskamp et al., Reference Epskamp, Borsboom and Fried 2018a ) as estimation method because of the large size of the dataset. Model search works by setting edges to zero and using a stepwise algorithm to continuously estimate the model until the optimal model is identified (Epskamp, Reference Epskamp 2014 ). This technique uses Bayesian information criterion (BIC) obtained through estimating the maximum likelihood of sparsity.

In their original analyses, Hiver and Al-Hoorie ( Reference Hiver and Al-Hoorie 2020b ) tested for normality and found that their data were not multivariate normal both in skewness and kurtosis. For this reason, the network was estimated using Spearman correlations (Epskamp, Reference Epskamp 2014 ).

After estimating the model, we evaluated the stability of the network structure in terms of edge-weight accuracy using bootstrapping (see Epskamp et al., Reference Epskamp, Borsboom and Fried 2018a for an in-depth explanation of bootstrapping in psychological networks). We used 5,000 samples of the nonparametric bootstrap to assess the variability of the edge-weights. This step should always be performed (Epskamp et al., Reference Epskamp, Borsboom and Fried 2018a ) as any interpretation of the network becomes limited if the network is unstable (Burger et al., Reference Burger, Isvoranu, Lunansky, Haslbeck, Epskamp, Hoekstra, Fried, Borsboom and Blanken 2022 ). The results show a good overlap between the estimated model and the bootstrapped edge-weights, indicating that the network of Figure 1 is stable. The results of the nonparametric bootstrap can be viewed in the supplementary materials.

To assess the stability of the centrality coefficients, we again used bootstrapping. We used the case-dropping bootstrap, specifically developed to this aim (Epskamp et al., Reference Epskamp, Borsboom and Fried 2018a ). The case-dropping bootstrap assesses the stability of the order of centrality in subsets of the data, that is, after systematically dropping an increasing percentage of participants from the dataset. The centrality stability for “strength” centrality was estimated on a sample of 5,000 bootstraps, which resulted in a correlation stability coefficient ( CS- coefficient) of 0.52 for the “strength” centrality. This is above the 0.5 ( CS- coefficient) recommendation (Epskamp et al., Reference Epskamp, Borsboom and Fried 2018a ), which is why we conclude that the stability of node centrality in this network model is good. The results are presented in the supplementary materials.

Based on the centrality indices (see Figure 2 ), ought-to L2 self 2 is the most central component in the network model in Figure 1 in terms of node strength, followed by intended effort 5. The questionnaire items that correspond to these components are “ Studying English is important to me to gain the approval of my peers ” and “ English would be still important to me in the future even if I failed in my English course. ” This suggests that peer approval and perceived future importance of English play important roles in L2 motivation, as they are the strongest direct relationships with other motivational constructs in the system.

Figure 2. Centrality plots for the L2MSS network.

Note : Centrality plots for the network model of the L2MSS. Centrality measures are shown as standardized z-scores. The raw centrality indices can be found in the online Supplementary Materials.

In addition to node strength, we also computed node centrality indices based on closeness and betweenness. The closeness index “indicates a short average distance of a specific node to all other nodes” (Hevey, Reference Hevey 2018 , p. 311). In the network model, the nodes with the highest closeness are the five intended effort nodes. This is an interesting find and indicates that intended effort may have an integral role in L2 motivation. Although the role of central components is not yet fully understood, it is thought that central nodes with high closeness are the most likely to both effect changes and be affected by changes in the system (Hevey, Reference Hevey 2018 ). The third measure of centrality, betweenness, refers to how well one node connects other nodes together; nodes with high betweenness lie on the shortest path between pairs of nodes. As shown in Figure 2 , the node with the highest betweenness is intended effort 5, followed by ought-to L2 self 5 and ideal L2 self 1.

Interpreting the network model

Both You et al. ( Reference You, Dörnyei and Csizér 2016 ) and Hiver and Al-Hoorie ( Reference Hiver and Al-Hoorie 2020b ) used SEM to evaluate the relationships between the L2MSS, vision, and intended effort. The network model contains four motivational constructs (ideal L2 self, ought-to L2 self, intended effort, visual style) and the two measures of L2 achievement (midterm grades and final exam grades). We can see the wider interconnectedness of components in the system, with multiple interactions across different motivational constructs.

One of the first things we notice when looking at this network model is that, although the motivational constructs are interrelated, there are only a few weak edges between any of the motivational constructs and the two measures of L2 proficiency. For example, final grades have a weak partial correlation with ideal self 1 (0.10) and midterm grades have a weak negative partial correlation with ought-to self 4 (–0.09). The network analysis results are consistent with Hiver and Al-Hoorie’s ( Reference Hiver and Al-Hoorie 2020b ) study, where the ideal L2 self was only a weak predictor of L2 achievement (accounting for less than 1% of the variance), and the ought-to L2 self had almost no predictive value.

Visual style

The visual style scale consists of five questionnaire items. As can be seen in Figure 1 , although each of the five measures of visual style are grouped together, the nodes are not as closely grouped together compared to nodes measuring other constructs. In Hiver and Al-Hoorie’s SEM analyses, they excluded visual style 2 to improve convergent validity, and also note that this scale had the lowest reliability in You et al.’s ( Reference You, Dörnyei and Csizér 2016 ) study. Removing items is typical with latent variable approaches, where researchers drop variables that do not load onto factors or if there are cross-loadings (Fried, Reference Fried 2020 ). With network analysis however, Fried ( Reference Fried 2020 , p. 21) has pointed out that “items that load onto two factors simultaneously make for the potentially most interesting items because they may build causal bridges between two communities of items.” Because of this, we decided to include visual style 2 in the network analysis. The network model shows that visual style 2 is linked to three other nodes measuring visual style, and also has a weak partial correlation with one measure of L2 achievement, on measure of the ideal L2 self, and one measure of intended effort. While visual style 2 was left out of the SEM analyses, results of the network analysis tentatively suggest that this questionnaire item may function as a bridge node between other motivational constructs. In both You et al. ( Reference You, Dörnyei and Csizér 2016 ) and Hiver and Al-Hoorie’s ( Reference Hiver and Al-Hoorie 2020b ) SEM analyses, they treated visual style as a predictor of the ideal L2 self and the ought-to L2 self. The network model is an undirected graph, so our analyses cannot provide additional insights into whether visual style is a predictor or outcome of motivation. What the network analysis does provide, is a more complex pattern of relationships between visual style and other system components than the original analyses. The nodes that measure visual style are partially correlated with components from all other motivational constructs in the network, as well as one measure of language achievement.

Intended effort

Besides the role of vision, You et al. and Hiver and Al-Hoorie were also interested in the direction of the relationship between intended effort and the L2MSS. Hiver and Al-Hoorie’s analyses of two competing SEM models showed that intended effort was a better predictor of the ideal L2 self and ought-to L2 self than an outcome. Previous research has provided empirical evidence for reciprocal causal relationships between motivation and academic achievement (Vu et al., Reference Vu, Magis-Weinberg, Jansen, van Atteveldt, Janssen, Lee, van der Maas, Raijmakers, Sachisthal and Meeter 2021 ). The network model shows that components of intended effort are related to components of all other subsystems, as well as L2 achievement, indicating a complex pattern of relationships. The results of the centrality indices highlight the overall importance of intended effort in L2 motivation, as the five intended effort variables have the highest closeness index in the network. Overall, intended effort 5 emerges as the most central component of the network. This item refers to the statement “ English would be still important to me in the future even if I failed in my English course. ” Intended effort 5 also has the highest centrality in terms of betweenness, and the second highest in terms of closeness and strength. The question surrounding the role of central components will be further discussed later in this article.

The second example illustrates how network analysis can be used to explore the relationships between multiple individual differences using the dataset from Dąbrowska’s ( Reference Dąbrowska 2018 ) study Experience, aptitude and individual differences in native language ultimate attainment. The dataset is publicly available online using the IRIS Database. The network model made from Dąbrowska’s ( Reference Dąbrowska 2018 ) dataset presents a different level of analysis from the previous example. In contrast to the network model in example 1 , where each node represents a single questionnaire item, each node in the network model in Figure 3 represents a distinct variable measured by aggregated task scores. In the original study, Dąbrowska tested the assumption that adult native speakers tend to converge on the same grammar. She addressed this question by considering two opposing approaches to language acquisition: the usage-based perspective and the modular perspective. From a usage-based perspective, language abilities are thought to emerge out of interactions between general cognitive mechanisms and exposure to linguistic input (Ellis & Wulff, Reference Ellis, Wulff, Miller, Bayram, Rothman and Serratrice 2018 ). From this perspective, “causal mechanisms interact iteratively to produce what appears to be structure” (Bybee & Beckner, Reference Bybee, Beckner, Heine and Narrog 2009 , p. 23). A usage-based approach is thus aligned with CDST, where linguistic knowledge emerges as a network of interrelated and interacting components. In contrast, from a modular perspective, language abilities are thought to stem from an innate universal grammar, whereby different types of language knowledge rely on autonomous modules within the mind (Tan & Shojamanesh, Reference Tan, Shojamanesh, Lutsenko and Lutsenko 2019 ).

Figure 3. A network model of individual differences in native language ultimate attainment.

Note : The nodes in this network are composite scores representing three measures of language proficiency and four individual differences. The three proficiency measures are receptive vocabulary, collocations, and grammatical comprehension. The four individual differences are nonverbal IQ, print exposure, language analytic ability, and years of education.

Dąbrowska ( Reference Dąbrowska 2018 ) discusses the plausibility of these two theories in connection with analyses of a dataset of 90 native English speakers’ performance on different linguistic and nonlinguistic tasks. She first analyzed the amount of individual variation on six tasks that measured grammatical comprehension, receptive vocabulary, collocations, nonverbal IQ, language analytic ability, and print exposure. Full details regarding which tests were used to measure each construct can be found in the original study. Dąbrowska then conducted Pearson correlations to explore interactions between the six aforementioned tasks as well as education (measured by number of years spent in education). This revealed several significant correlations between the measures of language knowledge as well as between other variables. To determine potential causes of individual differences in linguistic knowledge, Dąbrowska then conducted regression analyses with the four predictor variables (nonverbal IQ, language analytic ability, print exposure, and education) on each of the three measures of language knowledge. Overall, results showed that nonverbal IQ was strongly related to grammar and vocabulary, but not to collocations. Language analytic ability was also significantly related to grammar and vocabulary, as well as several other variables. Print exposure contributed more to vocabulary and collocations than to grammar, and education only weakly predicted each measure of language knowledge. Based on the significant correlations between the three measures of language knowledge and the fact that the same nonlinguistic variables predicted different areas of language knowledge, Dąbrowska concluded that these findings support a usage-based approach.

Figure 3 is a GGM of partial correlations that includes the same seven variables used in Dąbrowska’s analyses. The network model was estimated using the “least absolute shrinkage and selection operator” (LASSO), which is considered an appropriate estimation method for smaller datasets (Epskamp et al., Reference Epskamp, Borsboom and Fried 2018a ; Hevey, Reference Hevey 2018 ). The LASSO technique results in a sparser network, using only a relatively small number of edges to explain the covariance in structure (Epskamp et al., Reference Epskamp, Waldorp, Mõttus and Borsboom 2018b ). This makes the estimated model more interpretable and accurate, as very small edges are removed from the estimated network (Epskamp et al., Reference Epskamp, Borsboom and Fried 2018a ; Hevey, Reference Hevey 2018 ). The LASSO applies a regularization technique that is controlled by a tuning parameter. The tuning parameter was selected by minimizing the Extended Bayesian Information Criterion (EBIC), for which we used the default setting of 0.5.

To assess network stability, we used a nonparametric bootstrap of 5,000 samples. Bootstrapping results can be found in the supplementary materials. The bootstraps show wide 95% confidence intervals, meaning that the estimated network structure is not very stable and the found links should be interpreted with care. As such, our discussion and interpretation of this network model is tentative, and a larger sample size is needed to draw any strong conclusions. We did not compute centrality indices for this dataset because the aim of this network analysis was to explore overall patterns of relationships between variables, and also given the small number of variables in this model.

The network model in Figure 3 illustrates a complex system of interdependent relationships between linguistic and nonlinguistic variables. Each node in the network model in Figure 3 represents a composite variable. For example, the node “collocations” consists of 40 multiple choice items on the Words That Go Together test, and the node “print exposure” consists of 130 items on the Author Recognition Test. From a CDST perspective, the network model in Figure 3 provides a visualization of how different aspects of language knowledge are related to both internal resources (nonverbal IQ and language analytic ability) and external resources (print exposure and education). When comparing to the results of the regression analyses in the original study, the network model reflects the same overall patterns of relationships between individual differences in language knowledge. For example, nonverbal IQ is more strongly associated with grammar and vocabulary than with collocations, and print exposure is more strongly associated with vocabulary and collocations than with grammar. The fact that both analyses reveal the same overall patterns is not surprising because partial correlations and multiple regression coefficients both estimate of the strength of relationships between variables while controlling for the effects of other measured variables (Hevey, Reference Hevey 2018 ). The key difference is that regression analysis imposes unidirectional causal relationships between specific variables selected by the researcher, whereas with network analysis there are no assumptions regarding the direction of the relationships.

There are some subtle differences between the results of the network analyses and Dąbrowska’s analyses. For instance, whereas Dąbrowska found that language analytic ability was significantly related to both grammar and vocabulary, the network analysis shows that language analytic ability is only very weakly associated with vocabulary. In the network model, the relationship between language analytic ability and vocabulary knowledge appears to be altered by print exposure and nonverbal IQ. Similarly, while Dąbrowska’s analyses showed that education weakly predicted each measure of language knowledge, the network analysis shows that the relationship between education and language knowledge becomes weaker after controlling for the effects of print exposure, nonverbal IQ, and language analytic ability. It is also interesting to note that in the network model, the negative relationship between print exposure and nonverbal IQ becomes stronger after controlling for other variables. Another minor difference is that network analysis revealed a negative relationship between nonverbal IQ and print exposure whereas in Dąbrowska’s analyses this relationship was positive. The reason for this difference is that Dąbrowska transformed the raw IQ scores into percentages, while we opted to conduct analyses with the raw IQ scores. To confirm this, we conducted Pearson correlations between print exposure and both the raw and transformed IQ scores that showed that print exposure had a weak negative correlation with raw IQ scores (r(88) = –.03, p = .719) and a weak positive correlation with transformed IQ scores (r(88) = .08, p = .440). However as these are very small differences, they cannot be interpreted as meaningful. These slight differences revealed by the network analysis could be due to the fact that we included all seven variables in the network analysis, whereas Dąbrowska conducted three separate regression analyses for each measure of language knowledge. By taking a more holistic approach including all variables within the same analysis, additional patterns of relationships were revealed. This then raises the question of how many variables should be included when working from a CDST perspective.

Adding age to the network model

To explore this idea, we expanded on the original study by adding the variable “age” to the network model. Participants’ ages were contained within the original dataset that is available online, but Dąbrowska did not include this variable in her analyses. It seemed particularly interesting to include this variable because Dąbrowska used the dataset to evaluate the usage-based approach and the modular approach to language acquisition. Age is an indirect measure of language experience. With first language development, it is logical to assume that the older a person is, the more exposure to linguistic input they have. Thus, from a usage-based perspective, we might hypothesize age to be significantly related to a number of other variables, including measures of language knowledge. The 90 participants in Dąbrowska’s study varied greatly in age, with a range of 17 to 65 and a mean age of 38. The network model in Figure 4 is a GGM of partial correlations between eight variables (the seven variables from the original analyses plus age). The model was made following the same procedures described for the network model in Figure 3 . Similarly to the model without age, the bootstraps show wide 95% confidence intervals, meaning that the estimated network structure is also not very stable and the found links should be interpreted with care.

Figure 4. A network model of individual differences in language knowledge, including age.

Note : In addition to the same variables as the network model in Figure 3, this model also has the variable age. Blue edges denote positive partial correlations and red edges denote negative partial correlations.

The network model in Figure 4 shows that age is partially correlated with all other variables. Out of the three measures of language knowledge (grammar, vocabulary, and collocations), age is most strongly linked to vocabulary (0.35), which is the strongest positive edge in the network. Footnote 1 This is in line with previous studies which have shown that vocabulary is typically the only aspect of language knowledge that does not tend to decline with age (Reifegerste, Reference Reifegerste 2021 ). As could be expected, age is also related to print exposure. Age has a negative association with nonverbal IQ and language analytic ability, which is consistent with previous research on cognitive decline and aging (Reifegerste, Reference Reifegerste 2021 ). There is also a negative relationship between age and education, which is logical considering that the percentage of university attendance has increased over the years. Overall, the considerable effect that age has on the system provides tentative support for the usage-based approach. Using network analysis, we can visualize individual differences in language abilities as a complex system. While we cannot draw conclusions about emergent processes from cross-sectional data, based on this network model, we could speculate that vocabulary knowledge emerges out of interactions between cognitive abilities (nonverbal IQ) and other language experience (print exposure) throughout the lifespan (age).

In addition, controlling for age alters the partial correlations between other nodes. For example, in the model that includes age, vocabulary knowledge has a weak positive relationship with grammar (0.11) and language analytic ability (0.12), whereas in the model without age, these relationships are weaker (0.06 and 0.05). This indicates that age is a moderating variable. When controlling for age, the edge weight between grammar and language analytic ability is stronger (more positive) because age has negative partial correlations with grammar and language analytic ability. In a similar way, age also moderates the relationship between IQ and print exposure; these variables have an edge weight of –0.43 without age, and –0.26 when age is added to the model. In this case, the edge weight between IQ and print exposure is weaker (less positive) when controlling for age because age has negative partial correlations with IQ and print exposure.

Although the network models estimated in example 2 are not stable, and a larger sample size is necessary to draw any firm conclusions, our examples serve to illustrate how network analysis can be used to model multiple individual differences in language learning from a CDST perspective. The network analyses support the same conclusions as the original study (Dąbrowska, Reference Dąbrowska 2018 ), but rather than analyzing unidirectional relationships between individual difference constructs, the undirected network models in example two depict hypothesized multicausal relationships between variables. By estimating partial correlations between all variables, network analyses also reveal a more complex network of relationships between variables than the original study’s regression analyses, offering additional insights into the data.

We have provided two examples of how network analysis can be used to model complex systems from a relation-intensive perspective. These examples serve to illustrate how a network approach can offer new insights into which components form a system and the nature of the relationships between components. Network analysis is conceptually aligned with CDST, enabling us to model hypothesized multicausal relationships between variables. We have shown how network analysis of cross-sectional data can be used to model individual difference constructs as complex systems, viewing the network as a snapshot of (part of) a system in time. We illustrated this in example 1 with nodes at item level, to analyze motivational constructs on a micro level, and in example 2 with node at composite level, to analyze the relationships between individual differences and language knowledge on a more macro level. In both examples, network analysis complements the original analyses by providing a more intricate pattern of relationships between system components, and deeper understanding into the variables of interest.

Besides the examples of psychological network analysis in this article, there are other applications of network analysis that could also be beneficial to SLA researchers, such as the network comparison test and dynamic network analysis. It is also important to acknowledge that psychological network analysis is still a relatively new statistical technique, and there are some unanswered questions regarding how certain aspects of CDST fit with network analysis, for example regarding the question of how many variables to include and the role of central components. In the following section, we discuss some of these questions and highlight additional applications of network analysis that could be applied to SLA research.

The network comparison test

The network comparison test is an application of network analysis that can be used to compare group differences. The network comparison test statistically compares the networks of two (or more) groups, such as in terms of node centrality and global strength (van Borkulo et al., Reference van Borkulo, Boschloo, Kossakowski, Tio, Schoevers, Borsboom and Waldorp 2022 ). Networks can also be compared visually, which is typically done by constraining the layout of the two models for ease of visual comparison. Blanco et al. ( Reference Blanco, Contreras, Chaves, Lopez-Gomez, Hervas and Vazquez 2020 ) used a network comparison test to compare the effects of two different interventions on treating depression. One group of patients ( n = 45) received a 10-week Positive Psychology Intervention (PPI) while another group ( n = 48) received a 10-week Cognitive-Behavioral Therapy (CBT) program. Both groups completed clinical assessments of depression symptoms before and after the intervention treatments. Blanco et al. ( Reference Blanco, Contreras, Chaves, Lopez-Gomez, Hervas and Vazquez 2020 ) used this data to create two network models to compare before and after treatment. Results of the network comparison test showed that only the PPI group showed significant changes in several edge weights and global strength after intervention. In SLA research, the network comparison test could be used to statistically compare the networks of learners at different proficiency levels, at different time points, or across learning conditions. Both You et al. ( Reference You, Dörnyei and Csizér 2016 ) and Hiver and Al-Hoorie ( Reference Hiver and Al-Hoorie 2020b ) conducted additional analyses to compare the roles of vision and intended effort across male and female L2 learners. This comparison could be also done using a network comparison test. As such, the network comparison test could strengthen CDST inspired research by providing a means for hypothesis testing and generalizations. Comparing networks across groups could also help to ascertain the phenomenological validity of conceptualizing abstract psychological phenomena as complex systems. In addition, the network comparison test could provide insight into how to influence systems’ behavior, as illustrated by Blanco et al. ( Reference Blanco, Contreras, Chaves, Lopez-Gomez, Hervas and Vazquez 2020 ), and could a useful tool for SLA researchers considering complex interventions (Hiver et al., Reference Hiver, Al-Hoorie and Evans 2022 ).

Dynamic network analysis

In examples 1 and 2 , we took a relation-intensive CDST approach by estimating GGMs of cross-sectional data. The GGM can also be used with time-intensive and time-relation intensive research designs, for single subjects and group data, respectively. Dynamic network analysis requires intensive repeated measurements of variables, such as with a time-series or panel design, typically obtained through Experience Sampling Method (ESM), whereby participants provide self-reports at regular intervals during the day (Bringmann et al., Reference Bringmann, Vissers, Wichers, Geschwind, Kuppens, Peeters and Tuerlinckx 2013 ). With single-subject data, auto regressive (AR) modeling can model time dynamics within an individual by regressing one variable on a previous measurement of the same variable (called a lagged variable). The vector auto regressive (VAR) model is the multivariate extension of the AR model, where “a variable is regressed on all the lagged variables in the dynamic system” (van Bork et al., Reference van Bork, van Borkulo, Waldorp, Cramer, Borsboom and Wixted 2018 , p. 18). The VAR model has two extensions: graphical VAR and multilevel VAR. For single-subject data, graphical VAR can be used to create both temporal and contemporaneous networks using the GGM (Epskamp et al., 2018). Temporal networks have directed edges and show how the state of variables at one time point influence the state of variables at the next time point. A contemporaneous network model shows how variables predict each other at the same measurement occasion, after accounting for temporal effects (Epskamp et al., Reference Epskamp, Waldorp, Mõttus and Borsboom 2018b ), similarly to GAMMs and LCGMs. Multilevel VAR modeling can be used to model both within-group and between-group variance over time (Bringmann et al., Reference Bringmann, Vissers, Wichers, Geschwind, Kuppens, Peeters and Tuerlinckx 2013 ). For example, Bringmann et al. ( Reference Bringmann, Vissers, Wichers, Geschwind, Kuppens, Peeters and Tuerlinckx 2013 ) combined VAR and multilevel VAR to follow 129 participants’ changes in depressive symptoms during a treatment intervention, modeling time dynamics at the individual and group level.

In the field of clinical psychology, researchers are exploring how dynamic network modeling could provide insight into how people develop disorders over time, with the aim of using this knowledge to target group and/or individual treatment interventions (Bringmann et al., Reference Bringmann, Vissers, Wichers, Geschwind, Kuppens, Peeters and Tuerlinckx 2013 ; David et al., Reference David, Marshall, Evanovich and Mumma 2018 ; van Bork et al., Reference van Bork, van Borkulo, Waldorp, Cramer, Borsboom and Wixted 2018 ). Dynamic network analysis could also prove to be a useful methodology for CDST researchers in applied linguistics, and a few SLA studies have used ESM. For example, Waninge et al. ( Reference Waninge, Dörnyei and de Bot 2014 ) micro-mapped the motivational dynamics of four learners during their language lessons. They took measurements at 5-minute intervals throughout lessons, resulting in 10 observations per class. Similarly, Khajavy et al. ( Reference Khajavy, MacIntyre, Taherian, Ross, Zarrinabadi and Pawlak 2021 ) used ESM to examine the dynamic relationships between willingness to communicate (WTC), anxiety, and enjoyment of 38 students throughout six language lessons. Students indicated their level of WTC, anxiety, and enjoyment on a scale of 1 to 10 at 5-minute intervals, resulting in 10 observations per class. Gregersen et al. ( Reference Gregersen, Mercer, MacIntyre, Talbot and Banga 2020 ) also used ESM to explore the dynamics of language teacher well-being, where teachers used an app to respond to a short survey 10 times a day for 7 days. Although smartphone technology has the potential to use ESM more easily than in the past (Arndt et al., Reference Arndt, Granfeldt and Gullberg 2021 ; Gregersen et al., Reference Gregersen, Mercer, MacIntyre, Talbot and Banga 2020 ), it is still extremely challenging in most applied linguistics research settings to obtain a large enough number of observations to conduct a dynamic network analysis. For example, in the study by Bringmann et al. ( Reference Bringmann, Vissers, Wichers, Geschwind, Kuppens, Peeters and Tuerlinckx 2013 ), participants recorded depressive symptoms 10 times a day for 12 days, which resulted in a total of 120 observations per participant.

Nonlinearity

GGMs and VAR models are estimated based on assumptions of multivariate normality that assume linear relationships between variables (Epskamp et al., Reference Epskamp, Waldorp, Mõttus and Borsboom 2018b ). As such, these models may not present a fully accurate view of the data if the relationships between variables are nonlinear. For cross-sectional data, the Ising model is a nonlinear model used for binary variables (Finnemann et al., Reference Finnemann, Borsboom, Epskamp and van der Maas 2021 ), but nonlinear models for continuous variables have not yet been developed. For longitudinal data, while VAR models fit linear effects, new types of network analysis have been developed that can also capture nonlinear relationships between variables (Haslbeck et al., Reference Haslbeck, Bringmann and Waldorp 2021 ). The findings from several CDST studies with a time element have shown that language development, and its relationship with individual differences, is nonlinear (Fogal, Reference Fogal 2022 ; Pfenninger, Reference Pfenninger 2020 ; Piniel & Czisér, Reference Piniel, Csizér, Dörnyei, MacIntyre and Henry 2014 ). This is why some CDST research designs that include a time element are using techniques such as GAMM instead of LGCM, as GAMM can handle nonlinearity (Pfenninger, Reference Pfenninger 2020 ). Researchers in the field of network psychometrics have recently combined the VAR model with a Generalized Additive Model (GAM) framework, to estimate time-varying VAR models (Haslbeck et al., Reference Haslbeck, Bringmann and Waldorp 2021 ). The field of network psychometrics is developing rapidly and is likely to produce other useful techniques in the future that could further enrich our methodological toolbox.

Latent network analysis

In the first example of the L2MSS, we compared Hiver and Al-Hoorie’s ( Reference Hiver and Al-Hoorie 2020b ) SEM with our network analysis. For the past 100 years, psychological constructs have been studied using latent variable approaches, which assume that observed variables correlate because they reflect the same underlying construct (van Bork et al., Reference van Bork, Rhemtulla, Waldorp, Kruis, Rezvanifar and Borsboom 2019 ). Network analysis has been put forward as an alternative to latent variable approaches. From a network perspective, correlations between observed variables may reflect mutual interaction between psychological processes (van der Maas et al., Reference van der Maas, Dolan, Grasman, Wicherts, Huizenga and Raijmakers 2006 ). Although these two approaches have different competing causal explanations for the covariance between observed variables, both create models for variance-covariance matrices and are thus statistically equivalent (van Bork et al., Reference van Bork, Rhemtulla, Waldorp, Kruis, Rezvanifar and Borsboom 2019 ; van der Maas et al., Reference van der Maas, Dolan, Grasman, Wicherts, Huizenga and Raijmakers 2006 ). Because of this statistical equivalence, researchers have explored the idea that combining these two approaches could be complementary, resulting in latent network analysis (Golino & Epskamp, Reference Golino and Epskamp 2017 ; Guyon et al., Reference Guyon, Falissard and Kop 2017 ). Conceptually, a combined approach assumes that manifestations of psychological attributes have a common cause (latent variables) and that these latent variables interact (as a complex system) (Guyon et al., Reference Guyon, Falissard and Kop 2017 ). For example, Epskamp et al. ( Reference Epskamp, Rhemtulla and Borsboom 2017 ) have used latent network modeling to explore the structure of interdependent relationships between latent variables. An advantage of latent network analysis is that due to the incorporation of factor-based statistical techniques, it is possible to test model fit against data, which is a limitation of psychological network analysis (Epskamp et al., Reference Epskamp, Rhemtulla and Borsboom 2017 ; van der Maas et al., Reference van der Maas, Kan, Marsman and Stevenson 2017 ). It can also be considered a useful way of exploring latent variables within a dataset because clusters in the network can tell us about the factor structures present, without having to impose the direction of the relationship like SEM (Golino & Epskamp, Reference Golino and Epskamp 2017 ). Latent network analysis can be used with cross-sectional data as well as time-series and panel data.

The role of central components

In example 1 , we computed centrality indices for the network model of the L2MSS, which showed that the intended effort nodes have the highest centrality. Researchers from different fields have questioned whether central components have predictive ability and can be used to target interventions. The role of central components has so far provided insights into the dynamic processes of genetic networks, cortical networks, and ecosystems (for a detailed description see Rodrigues, Reference Rodrigues and Macau 2019 ). In the field of clinical psychology, findings from few studies indicate that central components could be used to target treatment interventions and make predictions about diagnoses. For example, in clinical research on eating disorders, central components have been predictive of treatment dropout (Lutz et al., Reference Lutz, Schwartz, Hofmann, Fisher, Husen and Rubel 2018 ) and treatment outcomes (Elliott et al., Reference Elliott, Jones and Schmidt 2020 ). The idea behind using central nodes to target interventions is that these nodes are more likely to have bigger effects (either directly or indirectly) on the rest of the system compared to targeting a less central node (Rouquette et al., Reference Rouquette, Pingault, Fried, Orri, Falissard, Kossakowski and Borsboom 2018 ). Nodes with high closeness in particular are more likely to be affected by changes in other components of the system and are also more likely to trigger change.

From the first network model example in Figure 1 , intended effort had the highest node centrality in terms of closeness, suggesting that intended effort plays a key role in triggering the dynamic processes involved in L2 motivation. This fits with Hiver and Al-Hoorie’s ( Reference Hiver and Al-Hoorie 2020b , p. 86) idea that putting in the effort to learn a language results in dynamic interaction between motivational constructs and task demands.

However, readers should note that the use of centrality indices in psychological networks is much debated (Bringmann et al., Reference Bringmann, Elmer, Epskamp, Krause, Schoch, Wichers, Wigman and Snippe 2019 ). Centrality indices stem from social network analysis, whereby the relationship between components/nodes is known; the connections between nodes are observable. In comparison, in psychological networks the relationship between nodes is not directly observed, but is estimated, based on the strength of partial correlations between our measurements of psychological constructs. Bringmann and colleagues (Bringmann et al., Reference Bringmann, Elmer, Epskamp, Krause, Schoch, Wichers, Wigman and Snippe 2019 ) have advised researchers to interpret centrality measures with care, especially betweenness and closeness centrality, as they are difficult to interpret and are often unstable.

The number of variables to include

Complex systems are characterized by dynamic interaction between multiple internal and external subsystems (de Bot et al., Reference de Bot, Lowie and Verspoor 2007 ; Larsen-Freeman & Cameron, Reference Larsen-Freeman and Cameron 2008 ). However, given the theoretical and practical impossibilities of analyzing the complete interconnected of a whole system, CDST researchers have to find a balance between oversimplification and undersimplification. Larsen-Freeman et al. ( Reference Larsen-Freeman, Schmid, Lowie, Schmid and Lowie 2011 ) have pointed out that a main methodological concern for CDST researchers is drawing boundaries and defining what we conceptualize to be a “functional whole.” Yet, when conducting network analysis, Hevey ( Reference Hevey 2018 , p. 307) has reasoned that it is “critically important to measure such potential confounding variables to ensure that their effects are controlled for.” The network model of Dąbrowska’s ( Reference Dąbrowska 2018 ) dataset in example 2 that includes age illustrates Hevey’s reasoning, as age moderates the relationships between other system components. It is highly likely that there are also other confounding variables that have been omitted from the model, such as socioeconomic status, L2 knowledge and experience, gender, and other cognitive abilities. As with other types of modeling, adding further variables to the network model could have both predictable and unpredictable effects on the rest of the system. Yet from a CDST perspective, it is theoretically impossible to measure every component of a system. What network analysis can do, is capture at least part of a system. Thus, while we acknowledge the potential of a network approach to SLA and individual differences, it is important to be mindful of its limitations.

Generalizability

Generalizability is another debated topic in CDST research. Several researchers have pointed out the lack of generalizability of CDST studies and the lack of practical implications that CDST can currently offer to the field of applied linguistics (Hiver et al., Reference Hiver, Al-Hoorie and Evans 2022 ; Palloti, Reference Palloti 2022 ). Generalizability is a complex topic and is related to the distinction between idiographic and nomothetic methodological approaches. Idiographic approaches focus on the individual level with within-subject designs, analyzing intraindividual differences (Hamaker, Reference Hamaker 2012 ). Idiographic approaches use longitudinal data and process-focused analyses. In contrast, nomothetic approaches focus on the group level with between-subject designs, analyzing interindividual differences (Hamaker, Reference Hamaker 2012 ). Nomothetic approaches use cross-sectional data and product-focused analyses.

The majority of CDST studies to date have used idiographic approaches (Hiver et al., Reference Hiver, Al-Hoorie and Evans 2022 ) because it is difficult to generalize from cross-sectional models to individual dynamics. This concept is known as the ergodicity problem: The idea that group statistics cannot be generalized to the individual and vice-versa (Lowie & Verspoor, Reference Lowie and Verspoor 2019 ). As Molenaar ( Reference Molenaar 2004 , p. 225) has pointed out, “only under very strict conditions—which are hardly obtained in real psychological processes—can a generalization be made from a structure of interindividual variation to the analogous structure of intraindividual variation.” However, this does not mean that idiographic and nomothetic approaches are in competition (Salvatore & Valsiner, Reference Salvatore and Valsiner 2010 ). In fact, they can be viewed as complementary, or two sides of the same coin (Grice, Reference Grice 2004 ). When discussing the idiographic-nomothetic debate in relation to research on personality, Grice ( Reference Grice 2004 ) argued that:

Establishing the uniqueness of some person’s developmental history, attitudes, thoughts, behaviors etc., would require the negation of nomothetic principles. Conversely, establishing the validity of a nomothetic principle that holds for all people would require the study of individual persons, not simply aggregates of persons. A true study of personality is therefore necessarily idiographic and nomothetic. (p. 205)

Lowie and Verspoor ( Reference Lowie and Verspoor 2019 ) have illustrated this point in relation to SLA, by investigating the role of motivation and aptitude in both a group study and in 22 longitudinal case studies. Their analyses showed that while learners showed different intraindividual learning trajectories over time, there were overall similarities between learners in terms of motivation and aptitude.

While some have argued that the idiographic approach undermines generalization (Palloti, Reference Palloti 2022 ; Spencer & Schönen, Reference Spencer and Schöner 2003 ), others have argued that idiography is a way to pursue generalized knowledge (Salvatore & Valsiner, Reference Salvatore and Valsiner 2010 ). As Salvatore and Valsiner ( Reference Salvatore and Valsiner 2010 ) have claimed, idiography is “the pursuit of nomothetic knowledge through the singularity of the psychological and social phenomena ” [emphasis in original] (p. 820). It is also important to note that nomothetic refers to what can be generalized across a sample population (e.g., from aggregated cross-sectional data), not what can be taken as a general law across all populations (Hamaker, Reference Hamaker 2012 ). Hence, as with any other cross-sectional data analysis, results of network analysis can only tell us about the population from which the data was sampled and cannot be taken as a general law across all populations or all individuals.

That said, a network approach offers a structural perspective that is currently missing from CDST research in the field of SLA and enables us to expand our research agenda beyond idiographic approaches, time-intensive approaches (Hiver et al., Reference Hiver, Al-Hoorie and Evans 2022 ). Taking steps toward generalizable findings, network analysis provides a means to quantitatively analyze the relationships between multiple variables and assess the relative importance of each variable within the system. Compared to other statistical techniques such as SEM, an advantage of network analysis is that it does not require a priori assumptions about unidirectional causal relations, but instead it allows for (hypothesized) bidirectional interactions between variables. As previously mentioned, other applications of network analysis such as the network comparison test make it possible for SLA researchers to test hypotheses and assess the extent to which systems can be generalized across different learner populations. Although network analysis is still relatively new, some researchers in clinical psychology have set out to examine its methodological validity and to determine the most appropriate metrics for assessing similarities between samples (Borsboom et al., Reference Borsboom, Fried, Epskamp, Waldorp, van Borkulo, van der Maas and Cramer 2017 ; Funkhouser et al., Reference Funkhouser, Correa, Gorka, Nelson, Phan and Shankman 2020 ). Researchers have also begun to assess the extent to which network analytic tools can inform the design of intervention studies. For example, Henry et al. ( Reference Henry, Robinaugh and Fried 2020 , p. 2) have developed a statistical testing procedure to assess the efficacy of an intervention, “determining if the dynamical systems of different people have the same optimal intervention studies.”

In this article we provided a brief overview of research methods used by SLA researchers working within a CDST paradigm. We put forward network analysis as a way to model complex systems from a relation-intensive perspective and provided two examples of how to apply network analysis to two different datasets. In the first example we estimated a network model of L2 motivation, which provided a more fine-tuned picture of the potential relationships between motivational constructs compared to the original SEM analyses. In the second example we created a network model of individual differences in native language knowledge, showing how network analysis can model the interconnectedness of individual difference constructs and different aspects of language knowledge.

While CDST researchers have made considerable advances in describing language development and changes in individual differences over time, the potential of relation-intensive approaches has not yet been explored. Through our two examples of network models, we hope to have illustrated that cross-sectional data does have a place in CDST research, and that network analysis is a useful technique to add to the CDST toolbox.

To view supplementary material for this article, please visit http://doi.org/10.1017/S0272263122000407 .

Acknowledgments

We would like to thank Han van der Maas, Wander Lowie, and the three anonymous reviewers for their invaluable feedback and suggestions on an earlier draft of this manuscript.

The experiment in this article earned an Open Materials badge for transparent practices. The materials are available at https://osf.io/hjcvz/

1 We conducted the bootstrapped difference test to check whether the edges in the network significantly differ from each other, in the supplementary materials. The edge Age-Vocabulary is significantly stronger than the edge Age-Grammar, but not from the edge Age-Collocations knowledge. This means that the difference between these edges has to be interpreted with care.

Figure 1. A network model of the L2MSS and L2 achievement. Note : In this network model of the L2MSS, there are four motivational constructs: the ideal L2 self, the ought-to L2 self, intended effort, and visual style. Each node represents a questionnaire item. Ought-to L2 self has been measured with six questionnaire items, and the other motivational constructs with five questionnaire items. There are also two composite measures of L2 proficiency: L2_T1 (students’ mid-term grades) and L2_T2 (students’ final grades).

Figure 2. Centrality plots for the L2MSS network. Note : Centrality plots for the network model of the L2MSS. Centrality measures are shown as standardized z-scores. The raw centrality indices can be found in the online Supplementary Materials.

Figure 3. A network model of individual differences in native language ultimate attainment. Note : The nodes in this network are composite scores representing three measures of language proficiency and four individual differences. The three proficiency measures are receptive vocabulary, collocations, and grammatical comprehension. The four individual differences are nonverbal IQ, print exposure, language analytic ability, and years of education.

Figure 4. A network model of individual differences in language knowledge, including age. Note : In addition to the same variables as the network model in Figure 3, this model also has the variable age. Blue edges denote positive partial correlations and red edges denote negative partial correlations.

Freeborn et al. supplementary material

This article has been cited by the following publications. This list is generated based on data provided by Crossref .

• Google Scholar

View all Google Scholar citations for this article.

Save article to Kindle

To save this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle .

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

• Volume 45, Issue 2
• Lani Freeborn (a1) , Sible Andringa (a1) , Gabriela Lunansky (a1) and Judith Rispens (a1)
• DOI: https://doi.org/10.1017/S0272263122000407

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox .

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive .

Reply to: Submit a response

- No HTML tags allowed - Web page URLs will display as text only - Lines and paragraphs break automatically - Attachments, images or tables are not permitted

Your details

Your email address will be used in order to notify you when your comment has been reviewed by the moderator and in case the author(s) of the article or the moderator need to contact you directly.

You have entered the maximum number of contributors

Conflicting interests.

Please list any fees and grants from, employment by, consultancy for, shared ownership in or any close relationship with, at any time over the preceding 36 months, any organisation whose interests may be affected by the publication of the response. Please also list any non-financial associations or interests (personal, professional, political, institutional, religious or other) that a reasonable reader would want to know about in relation to the submitted work. This pertains to all the authors of the piece, their spouses or partners.

Research Designs for Social Network Analysis

• Reference work entry
• First Online: 01 January 2018
• pp 2232–2239
• Cite this reference work entry

• Katarzyna Musial 3 , 4  

890 Accesses

Graph analysis ; Knowledge discovery in networks ; Social network mining

Social network analysis

Social network

a set of tools and methods that enable to analyze structures called social networks

a set of nodes and connections between nodes. Nodes may represent people, organizations, departments within organizations, or other social entities. Connections reflect interactions or common activities between nodes

Introduction

Research design for social network analysis (SNA), as for any other types of research, is a process during which the research question and set of methods that enable to answer the stated question are described. Social network analysis is a multidisciplinary research area, and in consequence a wide range of approaches to analyze network data exists. Nevertheless, each study in the field of social networks contains the following stages: (i) selecting sample, (ii) collecting data, (iii)...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save.

• Get 10 units per month
• Download Article/Chapter or eBook
• 1 Unit = 1 Article or 1 Chapter
• Cancel anytime
• Available as PDF
• Read on any device
• Instant download
• Own it forever
• Available as EPUB and PDF
• Durable hardcover edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Amaral LAN, Scala A, Barthelemy M, Stanley HE (2000) Classes of small-world networks. Proc Natl Acad Sci USA 97(21):11149–11152

Article   Google Scholar  

Barnes JA (1954) Class and committees in a Norwegian Island parish. Hum Relat 7:39–58

Breiger RL (2004) The analysis of social networks. In: Hardy M, Bryman A (eds) Handbook of data analysis. Sage, London, pp 505–526

Google Scholar  

Cattell V (2001) Poor people, poor places, and poor health: the mediating role of social networks and social capital. Soc Sci Med 52(10):1501–1516

Davis JA (1967) Clustering and structural balance in graphs. Hum Relat 20:181–187

Degenne A, Forse M (1999) Introducing social networks. Sage, London. MATH

Book   MATH   Google Scholar  

DiMicco J, Millen DR, Geyer W, Dugan C, Brownholtz B, Muller M (2008) Motivations for social networking at work. In: Proceedings of the computer supported cooperative work 2008 conference, San Diego. ACM, pp 711–720

Garton L, Haythorntwaite C, Wellman B (1997) Studying online social networks. J Comput-Mediat Commun 3(1). http://jcmc.indiana.edu/vol3/issue1/garton.html

Golbeck J, Hendler J (2006) FilmTrust: movie recommendations using trust in web-based social networks. In: Proceedings of consumer communications and networking conference, IEEE conference proceedings 1, Las Vegas, pp 282–286

Granovetter MS (1983) The strength of weak ties: a network theory revisited. Sociol Theory 1:201–233

Hanneman R, Riddle M (2005) Introduction to social network methods. Online textbook. Available from Internet: http://faculty.ucr.edu/~hanneman/nettext/ (01 04 2006)

Howard B (2008) Analyzing online social networks. Commun ACM 51(11):14–16

Kazienko P, Musial K (2006) Recommendation framework for online social networks. In: Proceedings of the 4th Atlantic web intelligence conference. Studies in computational intelligence. Beer-Sheva, Israel, pp 111–120

Krebs V (2000) The social life of routers. Internet Protoc J 3:14–25

Lazega E (2001) The collegial phenomenon. The social mechanism of co-operation among peers in a corporate law partnership. Oxford University Press, Oxford

Book   Google Scholar  

Liben-Nowell D, Kleinberg J (2003) The link prediction problem for social networks. In: Proceedings of the 12th international conference on information and knowledge management, New Orleans. ACM, pp 556–559

Montgomery J (1991) Social networks and labor-market outcomes: toward an economic analysis. Am Econ Rev 81(5):1407–1418

Morris M (1997) Sexual network and HIV. AIDS 11:206–219

Musial K, Kazienko P (2012) Social networks on the internet. World Wide Web J. https://doi.org/10.1007/s11280-011-0155-z

Newman MEJ (2001) The structure of scientific collaboration networks. Natl Acad Sci USA 98:404–409. MATH

Article   MathSciNet   MATH   Google Scholar  

Pagel M, Erdly W, Becker J (1987) Social networks: we get by with (and in spite of) a little help from our friends. J Pers Soc Psychol 53(4):793–804

Pool I, Kochen M (1978) Contacts and influence. Soc Netw 1(1):5–51. MathSciNet

Article   MathSciNet   Google Scholar  

Robins GL, Alexander M (2004) Small worlds among interlocking directors: network structure and distance in bipartite graphs. Comput Math Organ Theory 10:69–94. MATH

Article   MATH   Google Scholar  

Travers J, Milgram S (1969) An experimental study of the small world problem. Sociometry 32(4):425–443

Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press, New York

Yang WS, Dia JB, Cheng HC, Lin HT (2006) Mining social networks for targeted advertising. In: Proceedings of the 39th Hawaii international conference on systems science. IEEE Computer Society, Kauai, pp 425–443

Download references

Author information

Authors and affiliations.

Department of Informatics, King’s College London, London, UK

Katarzyna Musial

Department of Computing and Informatics, Bournemouth University, Poole, UK

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Katarzyna Musial .

Editor information

Editors and affiliations.

Department of Computer Science, University of Calgary, Calgary, AB, Canada

Reda Alhajj

Section Editor information

Department of Computer Science and Management, Institute of Informatics, Wrocław University of Technology, Wrocław, Poland

Przemysław Kazienko

Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland

Jaroslaw Jankowski

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Science+Business Media LLC, part of Springer Nature

About this entry

Cite this entry.

Musial, K. (2018). Research Designs for Social Network Analysis. In: Alhajj, R., Rokne, J. (eds) Encyclopedia of Social Network Analysis and Mining. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7131-2_246

Download citation

DOI : https://doi.org/10.1007/978-1-4939-7131-2_246

Published : 12 June 2018

Publisher Name : Springer, New York, NY

Print ISBN : 978-1-4939-7130-5

Online ISBN : 978-1-4939-7131-2

eBook Packages : Computer Science Reference Module Computer Science and Engineering

Share this entry

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

The PMC website is updating on October 15, 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• J Am Med Inform Assoc
• v.25(2); 2018 Feb

Applications of network analysis to routinely collected health care data: a systematic review

Jason cory brunson.

Center for Quantitative Medicine, UConn Health, Farmington, CT, USA

Reinhard C Laubenbacher

Associated data.

To survey network analyses of datasets collected in the course of routine operations in health care settings and identify driving questions, methods, needs, and potential for future research.

Materials and Methods

A search strategy was designed to find studies that applied network analysis to routinely collected health care datasets and was adapted to 3 bibliographic databases. The results were grouped according to a thematic analysis of their settings, objectives, data, and methods. Each group received a methodological synthesis.

The search found 189 distinct studies reported before August 2016. We manually partitioned the sample into 4 groups, which investigated institutional exchange, physician collaboration, clinical co-occurrence, and workplace interaction networks. Several robust and ongoing research programs were discerned within (and sometimes across) the groups. Little interaction was observed between these programs, despite conceptual and methodological similarities.

We use the literature sample to inform a discussion of good practice at this methodological interface, including the concordance of motivations, study design, data, and tools and the validation and standardization of techniques. We then highlight instances of positive feedback between methodological development and knowledge domains and assess the overall cohesion of the sample.

BACKGROUND AND SIGNIFICANCE

As electronic information systems have increased in capacity, efficiency, and accessibility, digitized clinical recordkeeping has made routinely collected health care data (RCHD) of unprecedented depth, scope, and variability available to researchers. The computer science revolution behind this progress has also facilitated the development and implementation of rapid, accurate algorithms to perform calculations on mathematical graphs and sample from distributions. This has led to an explosion in applications of network analysis (NA), which have proved successful in many domains at extracting conceptual insights and predictive power from large and messy datasets. A recent systematic review of data acquisition and analysis in systems medicine identified RCHD such as electronic medical records and public databases as the most common sources of data and NA as the most common modeling paradigm. 1 In this article, we review the work being done at the interface of these tools.

We set out to assess the motivations, substance, contributions, and needs of network analyses of routinely collected health care datasets (NARCHD): What problems have motivated this work, and what research programs have emerged? What has this research contributed to knowledge and methodology, and what further advances can be made? The paper provides a comprehensive survey of this literature and an evaluation of ongoing projects.

Our focus on methodologies complements several results-focused reviews that cover much of the same territory. Researchers seeking to build upon this knowledge base stand to benefit from a critical assessment of the methods in common use. By restricting our assessment to studies using data collected for nonresearch purposes, we showcase research designs that do not require collection of new data, which can be resource-intensive and require specialized expertise.

MATERIALS AND METHODS

Search strategy.

We operationalized our inclusion criteria as follows:

• health care–related data
• that were collected as part of routine operations
• and were not collected or demarcated as part of an intervention.
• modeled as mathematical graphs
• that were themselves objects of study
• investigated using tools from network analysis.

The search protocol is summarized in Figure 1 and detailed in the supplementary material . We omitted from consideration studies whose use of NA consisted in building artificial neural networks and Bayesian networks, which we felt were distinct subfields deserving separate treatment.

Search protocol and results. We based our keyword search on a “seed set” of publications that motivated our review, then adapted it to each database. Records were excluded based in most cases on title and abstract, and on full texts where necessary, though 8 desired full texts could not be found. Reference and citation chaining were performed twice in sequence (R, C, R, C).

Analysis process

While reading the final sample studies, we grouped them by commonality of study design, with an emphasis on the setting in which data were collected and the techniques used to analyze them, and to a lesser extent the motivating questions. When a study employed multiple datasets or analytical frameworks, we focused on the stage we identified as NARCHD. We then identified and described coherent research programs within each group. In addition to our qualitative analysis, we performed a scientometric summary, reported in the supplementary material . Both informed our discussion of the sample. Table 1 defines network terminology used throughout the sample and in our discussion.

Common network analysis terminology used in this manuscript

Our final sample comprised 138 journal articles, 52 conference presentations (papers and extended abstracts), 9 book sections, and 1 electronic preprint (see Figure 2 ). These 200 publications reported results from 189 distinct studies. In the sections below, we give an overview of each group and the major research programs within it, emphasizing projects that were primarily NARCHD.

Number of publications each year in our sample, using the earliest date known to have been available.

Institutional exchange networks

Fifty studies analyzed interorganizational health care systems as institutional exchange networks, the most common instantiation of which were patient-transfer and patient-sharing networks. Most of these studies took a network flow approach, 2 focusing on the movement of information and resources between providers, though several emphasized that established transfer patterns are an important part of health care infrastructure. 3 The studies sorted roughly into 2 investigative frameworks: interorganizational network analysis, 4 which views institutions as competitors and coordinators in a health care market and patient-sharing as a proxy for niche overlap or information exchange, and network epidemiology, which views patients as vectors for health care–associated infections. 5 , 6 This is reflected in a methodological divide, with static models employed on the economical side and dynamic simulation on the epidemiological side.

Major programs

One research program within this group focused on the role of interhospital patient mobility in improving outcomes and increasing efficiency. Some studies sought to explain patient transfers in terms of resource and performance differentials, geography, and other factors. 7–15 Others examined the structural positions of transfer partners 7 , 11 , 12 , 16 , 17 and investigated transfer patterns that suggested inefficiencies. 8 , 18 Another program tested theory-driven hypotheses of competitive interdependence, most notably similarities in performance between highly collaborative hospitals and in performance rankings between structurally equivalent ones. 16 , 19–25 Some additional studies measured the impact of market-based incentives on administrative decisions. 26 , 27 The largest program in the group examined how outbreaks spread through networks of patient transfer, referral, sharing, or interpersonal contact. Early observations that these networks had properties theorized to facilitate outbreaks 7 , 28 were followed by several simulation 29–36 and observational 37–41 studies of the structural determinants of infection spread and the viability of surveillance 42–45 and resource allocation 46 , 47 strategies.

Physician collaboration networks

Another group of 33 studies modeled institutional and regional physician communities as physician collaboration networks. These studies frequently took a network architecture approach, 2 emphasizing the determinants and effects of patient-sharing ties and motifs among doctors. This reflects the wider physician collaboration literature, which seeks to identify patterns associated with higher-quality care and better outcomes 48–50 and the dissemination of best practices. 49 , 51

Several studies in this group addressed the accurate measurement and prediction of patient-sharing. One compared the concordance of physician recollection and billing records 52 and others used demography, geography, affiliation, and attitudes at the physician or dyad level 53–58 and sociostructural tendencies 55 , 56 , 59 to account for shares and referrals. Another subset linked the motifs and meso-structure of patient-sharing networks to differences in physician practice, 59–63 patient outcomes, 56 , 64–70 and health disparities. 71 , 72

Clinical co-occurrence networks

A distinctive group of 59 studies concerned relational models of clinical events mined from patient- or encounter-level health records (clinical co-occurrence networks) most often used to generate etiological hypotheses. Half of these studies investigated graph models of disease co-occurrence, 73 , 74 often called comorbidity networks. Other studies investigated more general networks of diagnoses, lab tests, procedures, prescriptions, ingredients, and clinical terms mined from patient encounter notes. 75 Data mining and other exploratory methods dominated, with many techniques borrowed from other domains or developed ad hoc. Analyses were mostly local; only a handful invoked community structure or distance effects.

Three coherent programs emerged from the studies on disease graphs. One used disease co-occurrence to identify candidate disease dependencies for lab research. 76–82 Another assessed the ability of known genetic, 78 , 79 , 83–86 proteomic, 82 , 85 environmental, lifestyle, 87 or a combination of factors 87–89 to account for co-occurrences. A third aggregated patient timelines into temporal graphs , directed graphs in which links encode time differentials, that were used to describe patient trajectories and predict future diagnoses. 90–96 Several other studies employed clustering algorithms, in some cases to recapitulate formal disease ontologies, 84 , 96 , 97 but in others to develop risk-predictive measures, 98 improve standard classifications, 99 and stratify patients. 97 , 100 , 101

Workplace interaction networks

The remaining 47 studies fit into a highly modular group investigating workplace interaction networks, including network models of shared record access , interprovider communication , interpersonal contacts , and patient handoffs. Most of these studies were institution-specific and drew from health information system access or process logs. Dominant research themes used signature NA methods, eg, process mining to model workflow. 102 Some of these modules were integrated, by citation or common authorship, into 1 of the groups discussed previously. Most others lay within a larger literature on the social network analysis (SNA) of health care wards and teams. 103

A unique program appearing in this group concerned anomaly detection. These studies used data from user access logs and focused on inappropriate access to patient records 104–107 and fraud detection. 108 Another subset used similar datasets to model infection spread through contact networks. By incorporating patient-staff contact, 109 , 110 surveillance cultures, 109 and spatial proximity, 111 , 112 these studies extended the scope of the epidemiological studies discussed above. The largest program emerged from the process management literature. These studies used patient handoff data to characterize the interactions of care teams 113–117 and ward staffs, 118–122 and to identify prototypical clinical pathways. 107 , 120 , 123–128

The studies included in our sample took a wide range of approaches, summarized in Table 2 , which reflected differences in their conceptual and material needs. In this section we document some strengths and weaknesses of these studies and suggest some standards of good practice. We focus on 2 fronts: the choice of framework and the model construction and validation. We then discuss several achievements and needs, focusing on the mutual benefits to knowledge and methodology and on the overall cohesion of the sample.

Summary of conceptual and methodological frameworks of journal articles in our sample

Framework assignments were subjective, and rare assignments were combined for ease of reference. Every study incorporated (social) network analysis conceptually and methodologically; when we identified no more specific framework, we listed “NA.”

Choice of framework

Every analysis decision requires justification, starting with the choice of framework. The network conceptual model is most illustratively called into question in the clinical co-occurrence setting: There are widely recognized problems with collapsing co-occurrence data to unipartite network models, but few studies of the “diseaseome” addressed them. The most popular use of these models was visualization; indeed, several studies analyzed co-occurrence data geometrically, for instance by using hierarchical clustering rather than community detection, but visualized them as graphs. 97 , 101 , 169 Force-directed layout algorithms exploit the binary nature of graphs and can place unlinked dyads at any distance and orientation from each other; for count data such as these, visualizations like correspondence analysis biplots that minimize distortion are arguably more appropriate. 170 Additionally, a defining element of NA is the conceptualization of transmission channels as links and of functional dependencies as motifs, which predicts distance effects between nonadjacent nodes and dependencies between node attributes and neighborhood characteristics. These concepts do not follow as naturally from disease co-occurrence as from, say, patient-sharing. Some studies demonstrated the utility of visualizations for electronic dashboards, though only at the neighborhood level. 80 , 116 , 153 While a few studies made valuable use of distance effects 81 , 90 , 91 or motif mining, 84 most were primarily dyadic. Thus, despite their conceptual popularity, disease networks themselves have received little analytic attention.

Once a framework is adopted, consequential considerations remain, among them concordance between the theoretical constructs of interest and the measures used to detect them. In the (S)NA setting, some constructs will be structural, and the corresponding measures should be theoretically grounded. For example, early epidemiological studies identified features of contact and transfer networks known from existing work to have implications for infection spread. 11 , 28 Some studies employed network measures without specific motivation, eg, degree and betweenness centrality as possible social determinants of methadone treatment continuation. 166 In this case, a discernible effect of degree was given a reasonable interpretation, but an indiscernible effect of betweenness was not commented upon; had it been theoretically motivated, an account of this result would clearly be required. Occasionally, an SNA framing seemed incidental to the analysis being conducted. For example, the number of visits a doctor makes to a patient and the share of the visit costs coming from hospital claims might be expected to predict total visit costs by indicating severity of illness or resource use; when termed “connectedness” and “tie strength,” they instead suggested a causal relationship with care team coordination. 114 In this case, SNA theory seemed ill-suited to the hypotheses being tested.

Model construction and validation

Network models were constructed, with few exceptions, by linking nodes according to 3 data patterns: co-occurrence on records (physicians’ patients, patient diagnoses), sequential occurrence on chronological records (patient admissions and discharges, staff HIS access), and source/target designation on transmission records (patient transfers, staff handoffs). Higher-order multipartite structures were often reduced to simple graph models for conceptual or computational reasons. For example, early interorganizational analyses relied on network measures of collaboration and competition, for which chronological patient-hospital admission/discharge data were flattened to unipartite graphs. 16 , 19 , 20 , 23 , 25 More recent contributions expanded their scope to multilevel models of organizations and activities 26 and of organizations and their departments, 21 in both cases grounding the motifs of interest in theory and building statistical inference models around them.

Studies not strongly grounded in theory usually focused on machine learning–based prediction, using a wider range of motifs in higher-order incidence structures and developing efficient algorithms to mine for them. This is evident from several studies that mined these structures for recurring patterns indicative of standard protocols 128 , 171 or for deviations suggestive of security breaches 104 , 105 or fraudulent practices. 108 , 172

Studies collapsed higher-order incidence structures into more manageable graphs using various techniques, none of which have become domain standards. In the research program on physician patient-sharing, for example, different studies adopted different statistics and thresholds on 2 physicians’ shared patients for link determination, including raw counts, 70 mutual percentages, 55 caseload-relative thresholds, 54 and average numbers of visits by shared patients. 59 Graph properties are sensitive to these decisions, as illustrated by 2 inaugural studies that sought to quantify the number of alters with whom an ego physician must coordinate care. Based on shared Medicare patients for whom either ego or alter was deemed primary, a representative sample of physicians in the United States were found to have typically hundreds of peers. 133 In contrast, based on ego and alter seeing common patients at ≥1% each of their total visits, physicians within professional groups in Ontario had on average 2.2 peers. 143

A related concern is the dependence of graph models on data sources, each having its own scope, bias, and format. Comorbidity graphs were constructed using patient-level data from several institution-specific electronic health records (EHRs) 77 , 79 , 80 , 84 , 147 and from both public and private billing claims, 83 , 86 , 146 , 148 , 154 , 173 and using incident-level data from adverse event reports. 78 “Co-occurrence” itself ranged in meaning from a simple correlation 92 or odds ratio 146 to cosine similarity 97 , 101 to a statistical signal from a probabilistic model, 76 and the aggregated parts were not always dyads. 78 , 148 These models, of the same theoretical construct, were never directly compared.

A few validation studies did address such concerns. An early study of physician collaboration networks estimated the accuracy with which the number of Medicare patients 2 physicians share predicts their self-reporting of a professional relationship, using different raw-number thresholds, 52 and a follow-up study characterized physicians’ stated reasons for referring patients to their data-mined colleagues. 57 A similar study examined the decision process whereby clinical teams at sending hospitals maintained primary transfer relationships with recipient hospitals. 15 A later study of health care worker interactions compared the relative likelihood that patients’ records would be accessed by staff in different departments with those staff members’ expectations. 122 By drawing from nationwide patient admission datasets from 2 countries, 1 study of infection surveillance was able to report on the robustness of their optimal strategy to the difference between the health care systems. 43 With respect to disease graphs, 2 studies compared the sets of comorbid pairs identified using the same link determination rule on multiple datasets, 79 , 86 and 1 matched observed comorbidities with co-occurrences in the medical literature. 165 Several additional studies discussed biases in their data and tested the sensitivity of their results to different sources and thresholds, but these efforts were far narrower than the breadth of methods used, and none discussed concomitant differences in the resulting network structure.

Knowledge gains and methods development

Several studies used (S)NA to advance knowledge in ways that other methods would not be expected to, eg, invoking distance effects and motifs. Here is a partial list:

• An investigation of hospital transfers identified “cascades” of inefficiencies, measured as temporal paths through a transfer network in which a transfer by one sending hospital to a nonprimary recipient apparently results in a primary sending partner of the recipient redirecting a transfer of its own, and so on. 18
• One approach to accounting for population comorbidities using genetic commonalities was to perform a triad census on the multilevel network of population comorbidities and genetic overlaps. 84 Another was to select diseases of high betweenness with respect to 2 index diseases (obesity and colorectal cancer) and identify their shared genetic associations. 81
• One application for co-occurring clinical text fields was to distinguish “phenotypic signatures” of mental illnesses, which pose difficulties for criteria-based diagnosis. 140
• A study of operating room staff interactions following a layout redesign observed a shift from sequential to parallel performance of perioperative tasks, suggesting new vulnerabilities to staffing changes. 120
• A study in a neonatal intensive care unit linked longer handoff cycles to lower reported patient satisfaction, suggesting a quantitative measure of care continuity. 121

Despite its inherent limitations, RCHD was likewise often well-suited to a study’s needs. One instance was the rigorous testing of hypotheses about interorganizational collaboration and competition derived from economic theory, which was made possible in the health care sector by the exceptionally thorough and reliable documentation on both information and resource exchange (patient transfers) and quality of performance (discharge rates or lengths of stay) contained in administrative datasets. 19 , 23 Another was the use of empirical data on institutional infection rates or individual cultures by several inter- 29, 31 , 34 , 37 , 40 , 45 and intraorganizational 109 , 155 epidemiological modeling studies, respectively, to calibrate or validate their network models. Third, patient-sharing networks provided an exceptionally detailed setting in which the social diffusion of practice could be measured. 59 , 61 , 62 These studies focused on relationships between structural and attributive variables, which often require considerable expense and effort to generate but are common elements of RCHD.

Conversely, though most studies used NA tools “out of the box,” several domain-specific research questions led to advances in methodology, attesting to the reciprocal value to network science of health care applications. The need to adapt individual-level epidemiological models to populated institutions led to fractional models of immunization, 47 and the simulation framework (and sometimes the software) developed for these studies was also used to test surveillance 42–45 and resource allocation 46 , 47 strategies. Predictive modeling of population comorbidity spurred the development of tools for exploration, link prediction, and stratification in multilayer disease networks combined from EHR and molecular data. 84 , 87 , 88 Efforts to model disease progression and clinical workflow inspired several original aggregations of ordered pairs and longer chronological disease sequences into temporal graphs, 90 , 91 , 128 , 174 a procedure still young in network science. 175 In the domain of interorganizational networks, the availability of exceptionally thorough and reliable documentation on patient admissions and transfers made health care a testing ground for novel graph-theoretical statistical inference methods, including new specifications of ERGMs, 16 , 25 extensions to stochastic actor-oriented models, 26 and adaptations of multiple membership–multiple classification models to multilevel networks. 21

While research at this interface shows no signs of slowing ( Figure 2 ), a scientometric analysis (see supplementary material ) showed that the literature is highly fragmented, roughly along the groups identified above. The research programs identified above often had “home journals” where several research teams published, for instance Medical Care for physician collaboration and Infection Control and Hospital Epidemiology for patient transfer epidemiology, but we found very little overlap in venues between programs, and no central hub for NARCHD. Several early publications that anticipated the approaches that later gained traction were not cited by any others in our sample, 9 , 10 , 13 , 113 , 123 , 143 , 161 , 176 , 177 nor did they have any authors in common with them (until recently 79 ). Seldom, too, did active teams form new collaborations. 86 , 174 , 178 A stepwise ERGM of the graph of citations failed to explain the extent of fragmentation based on publication dates, common authorship, and simple generative processes. 179 , 180

This fragmentation is not so surprising from a young field, but is also in part an artifact of our review criteria. The cohesive research programs described above, as evidenced by several domain-focused reviews, 5 , 6 , 48–51 , 74 , 75 , 102 , 103 , 181 , 182 are merely the contours along which much larger research programs intersect our sample. The vast majority of SNA in health care settings relies on original survey data, 103 and the scale of the health care environment amenable to network modeling far exceeds that of RCHD. 183 Our sample may therefore underestimate the cohesion of this research community.

We did observe several instances of corroborations and useful comparisons with previous work. Several regression and ERGM analyses (and some visual inspections) observed that patients tended to be transferred to target hospitals with more care-relevant resources 7–10 and better patient outcomes, 8 , 11–13 and the best-equipped and -performing target hospitals tended to be more central. 7 , 11 , 17 Transfer partnerships were reliably associated with competitive interdependence, even after controlling for geography, attributive similarity, and generative processes. 16 , 23 , 24 Several interorganizational epidemiological studies corroborated associations between a hospital’s in-degree and infection rate 29–31 , 34 , 40 , 41 and between its overall connectedness and overall pathogen prevalence 30 , 33 , 37 (with 1 exception 35 ).

Some applications saw interestingly inconsistent results: One study identified cohesive communities from the commonalities in conditions diagnosed by an institution’s providers, which reflected departmental structure in some ways but not others. 161 Another study mined access logs to produce a communication network dominated by multispecialty teams, more consistent with cohesive floor staff and service teams, 129 and a third observed from a similar dataset that collaboration was more prevalent within departments than between them. 162 How best to identify and characterize cohesive units from institution HIS data appears to be an open question.

Yet researchers in different domains faced many similar challenges, and opportunities may have been missed to build upon each other’s progress and to recombine techniques developed independently. A case in point is the aggregation of temporal sequences of clinical events into a directed graph. From a clinical informatics perspective, Patnaik et al. 174 explored a top-down approach starting with a partial order on a collection of diagnosis and procedure codes, before Hanauer and Ramakrishnan 93 (of the same team) adopted a bottom-up approach of statistically identifying individual temporal pairs. From a data security perspective, H. Zhang et al. 107 constructed a temporal graph from access logs for the purpose of characterizing routine behavior and identifying deviations from it, by aggregating all patient record–specific access sequences, analogous to Patnaik et al. At a more granular level, Nikfarjam et al. 149 developed a text-mining technique to encode clinical notes into encounter-level temporal graphs. From a prognosis perspective, Liu et al. 126 constructed similar patient-level temporal graphs from timelines of coded clinical events, which they clustered using feature extraction methods from linear algebra, and Jensen et al. 90 took the approach, an extension of Zhang et al.’s, of first clustering patient timelines and then aggregating these in each cluster into a cohort-level temporal graph. Meanwhile, more sophisticated tools to produce similar summary structures had been developed and implemented by business researchers for process management and applied to EHR process logs by a different community of researchers. 120 , 124 , 184–186 Y. Zhang et al. 128 proposed a clustering-based alternative to these standard tools, much in the spirit of Jensen et al., and Finney et al. 187 adopted an existing theoretical and methodological framework within which to contribute an efficient implementation. None of these studies cited those that came before (excluding the process mining studies).

In summary, the disconnectedness and inconsistency of this literature suggests the possible benefit to be gained from detailing how the motivating problems, study designs, data sources, and network tools reviewed here “hang together.”

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sector.

COMPETING INTERESTS

The authors have no competing interests to declare.

CONTRIBUTORS

JCB and RL conceived and designed the review. JCB designed and conducted the search. JCB and RL designed, and JCB performed, the synthesis. JCB designed and performed the scientometric analysis. JCB and RL contributed to the discussion, wrote and approved the final manuscript, and take responsibility for the integrity of the work.

SUPPLEMENTARY MATERIAL

Supplementary material is available at Journal of the American Medical Informatics Association online.

Supplementary Material

Supplementary data, acknowledgments.

We thank Jenny Miglus for assistance in constructing and refining literature searches and 2 anonymous reviewers for suggestions that greatly improved the manuscript.

APPENDIX: CASE STUDIES

In an effort to structurally characterize hospitals that suffered the highest rates of methicillin-resistant Staphylococcus aureus (MRSA), Ohst et al. (2014) 34 drew upon a comprehensive regional dataset of care episodes to construct a contact network of care units based on patient transfers and to assign each unit a MRSA prevalence rate based on the observed frequency of positive tests. As candidate measures of each unit’s structural position, the authors used 5 notions of centrality: in-degree and daily patient turnover (based on immediate contacts), weighted and unweighted betweenness (based on shortest paths), and PageRank (based on random walks). The contact network evolved over time, so units’ centralities were calculated as of the time of each positive test. Averaging their results over the different strains of MRSA, the authors observed 2 paradoxical trends: more central units were more likely to have at least 1 positive test, but those that did had lower prevalence on average. This led the authors to conclude that the net relationship between centrality and prevalence has limited practical value. Simulations confirmed the relationship and further showed that the measures based on immediate contacts outperformed those based on geodesics (betweenness) or walks (PageRank), and were themselves outperformed by the network-agnostic attribute of patient turnover.

Moen et al. (2016) 59 provide a richly detailed case study of physician collaboration, as reconstructed on the basis of patient-sharing observed in Medicare claims. The authors tailored their analysis, including the selection of comparison regions, the sample of beneficiaries and physicians, and the choice of network measures and models, to the question of why regional health care networks differ in their adherence to evidence-based defibrillator guidelines. Building upon a literature with mixed emphasis on physician-, hospital-, and region-level network structure, they incorporated effects of individual and structural attributes at the physician and hospital levels. Their multistage design used a patient-level logistic regression framework with physician-level and hospital-level random effects, and incorporated as predictors of interest the hospital referral region and several hospital-, physician-, and patient-level covariates. Among these were estimated effects of homophily by physician specialty, controlling for the distribution of colleague counts (degree distribution), and any of several measures of the centrality of hospitals within the region and of physicians within hospitals. Among other findings, they concluded that physicians’ frequency of patient-sharing (node strength) and closeness centrality in their hospital together accounted for much of the variation between hospital referral regions, indicating that the social positions of physicians among their colleagues is important to their institution’s ability to articulate good practice.

In an early contribution, Davis and Chawla (2011) 84 demonstrated that data-driven structural analysis could generate useful targets for experimental investigation. From the medical histories of patients served by a regional health system, they constructed a multimorbidity graph in which a link between 2 diseases was weighted by mutual information. Analogously, they constructed a disease graph whose links indicated shared genetic factors, based on gene-disease associations compiled from the experimental literature. (The most frequent database used for this purpose is the Online Mendelian Inheritance in Man, www.omim.org .) Their analysis of the combined multilayer disease network yielded several results: First, population-level co-occurrence (“phenotypic links”) correlated strongly with known genetic overlap (“genetic links”), corroborating the genetic deterministic paradigm. Second, roughly the same subsets of nodes in both networks formed strongly linked communities, which recapitulated clinically meaningful disease groups. Finally, a probabilistic link prediction model, built on a generalization of the triad census, revealed that a combination of phenotypic and (known) genetic links achieved greater predictive accuracy of unknown genetic links than either source alone.

Zhang et al. (2013) 107 addressed a security problem that distinguishes EHRs from many other information systems: The frequency with which users will need to violate any manually curated set of access rules, in order to maintain patient care in hectic and unpredictable circumstances, makes postliminary auditing impractical. They proposed aggregating patient-specific sequences of EMR access into temporal graph models, for which they derived statistics to measure the irregularity of a given access or access sequence with respect to the corpus. Whereas the temporal graphs would be constructed iteratively from continually generated access logs, this approach is learning-based but relies on an assumption that care processes are consistent over time. A test of the method on an institutional EHR revealed that rates of irregularity, and of the success of their approach, varied across hospital services, accentuating the need to carefully tailor anomaly detection methods.

• iSchool Connect

Network Science and Network Analysis

Representing, analyzing, and modeling the structure and dynamics of complex social, scientific, and technological systems as networks or graphs; and using computational tools for identifying, explaining, and understanding the patterns they contain

Researchers Working in this Area

Related Research Projects

Career: using network analysis to assess confidence in research synthesis.

Policy in areas such as conservation, energy, healthcare, and sustainable development is informed by a variety of factors, including the best available science. Determining the best available science requires synthesizing multiple scientific results to gauge both the level of scientific consensus and the reliability of the research. However, on some policy-relevant topics, syntheses continue…

FABRIC Across Borders

Science is fast outgrowing the capabilities of today's Internet infrastructure. To fully capitalize on big data, artificial intelligence, advanced computation and the Internet of Things requires robust, interconnected computers, storage, networks and software. Uneven progress in science cyberinfrastructure has led to bottlenecks that stymie collaboration and slow the process of discovery.…

Identifying False HPV-Vaccine Information and Modeling Its Impact on Risk Perceptions

Human papillomavirus (HPV) is the most common sexually transmitted infection in the U.S., with over 34,000 new HPV-related cancers diagnosed annually, according to the Centers for Disease Control and Prevention. An HPV vaccine, which was approved by the Food and Drug Administration (FDA) in 2006, is recommended as part of routine vaccinations for school-aged children. However, the vaccine's…

Identifying Potential Bias in Science Using Citation Network Structures

Biased citation benefits authors in the short-term by bolstering grants and papers, making them more easily accepted. However, it can have severe negative consequences for scientific inquiry. The need for a bias detection tool is evident from previous studies on citation bias, but existing work lacks crucial elements needed to scale the underlying approaches. This project will test the…

Strengthening Public Libraries’ Information Literacy Services Through an Understanding of Knowledge Brokers’ Assessment of Technical and Scientific Information

Scientific and technical information is often translated for the public, by knowledge brokers such as journalists, Wikipedia editors, activists, and public librarians. This project will research how knowledge brokers assess the quality of scientific and technical information and the implications for public access, information literacy, and understanding of science. The project will use case…

News Stories

Project to study anti-black violence in newspapers receives support from mellon foundation.

A project to examine the circulation of newspaper reports about anti-Black violence in nineteenth- and early twentieth-century U.S. newspapers could provide context to the spread of white supremacist ideologies in social media today. 

Ma to join iSchool faculty

The iSchool is pleased to announce that Jiaqi Ma will join the faculty as an assistant professor in August 2023, pending approval by the University of Illinois Board of Trustees. Ma is a PhD candidate in School of Information at the University of Michigan (UMSI). He earned his bachelor's degree in automation from Tsinghua University. For the 2022-2023 academic year, he will be a postdoctoral fellow at Harvard University.

Dinh defends dissertation

Doctoral candidate Ly Dinh successfully defended her dissertation, "Advances to Network Analysis Theories and Methods for the Understanding of Formal and Emergent Structures in Interpersonal, Corporate/Organizational, and Hazards Response Setting," on May 19.

Cordell to deliver keynote on Viral Texts project

Associate Professor Ryan Cordell will deliver the keynote address at the Marbach-Weimar-Wolfenbüttel (MWW) Research Association Mid-Term Conference, which will be held virtually from Germany on October 14-15. The goal of the MWW is "to provide future-oriented impulses for collaboration in the field of humanities and cultural studies research." The association's mid-term conference will focus on engagement with material and medial losses in the archive and library.

New journal article examines vaccination misinformation on social media

Research conducted by Assistant Professor Jessie Chin's Adaptive Cognition and Interaction Design Lab (ACTION) provided the foundation for an article recently published in the high-impact Journal of Medical Internet Research . PhD student Tre Tomaszewski is the first author on the peer-reviewed article, "Identifying False Human Papillomavirus (HPV) Vaccine Information and Corresponding Risk Perceptions from Twitter: Advanced Predictive Models."

Schneider receives NSF CAREER award

Assistant Professor Jodi Schneider has received a National Science Foundation (NSF) CAREER award to assess how to identify potential sources of bias in research and how confident we can be in the conclusions drawn from a particular body of evidence. This prestigious award is given in support of early-career faculty who have the potential to serve as academic role models in research and education and to lead advances in the mission of their department or organization. Schneider's project, "Using Network Analysis to Assess Confidence in Research Synthesis," will be supported by a five-year, $599,963 grant from the NSF.

Model helps predict, analyze decision-making on adopting Type 2 diabetes medical guidelines

Health care workers often don't adopt new guidelines for best practices in medical care until well after those guidelines are established. A team of researchers led by Eunice E. Santos, the dean of the School of Information Sciences at the University of Illinois Urbana-Champaign, has developed a new computational modeling and simulation framework to analyze decision-making and identify effective dissemination strategies for medical guidelines.

Chin receives NIH grant for study of false HPV-vaccine information

Assistant Professor Jessie Chin has received a $389,810 grant from the National Institutes of Health (NIH) to identify false information about the HPV vaccine and model its impact on risk perceptions.

iSchool represented at Women in Data Science conference

iSchool faculty and students will present their research at the Women in Data Science Urbana-Champaign Conference (WiDS), which will be held on March 6 at the University of Illinois. The event, which is organized by the National Center for Supercomputing Applications (NCSA) and cosponsored by the iSchool, is one of over 200 WiDS conferences being held worldwide.

• Privacy Policy

Home » Social Network Analysis – Types, Tools and Examples

Social Network Analysis – Types, Tools and Examples

Table of Contents

Social Network Analysis

Social Network Analysis (SNA) is an analytical method used to study social structures through the use of networks and graph theory. It identifies the relationships between individuals, organizations, or other entities and examines the patterns and implications of these relationships.

The nodes in the network represent the actors within the networks and the ties or edges represent relationships between the actors. These might be, for example, friendship ties between people, business relationships between companies, or communication patterns between individuals.

By analyzing the network structure and the characteristics of the actors within the network, SNA can reveal properties such as the distribution of resources, the flow of information, or the overall connectivity of the network.

Here are a few key concepts in SNA:

• Centrality : This measures the importance of a node in the network. Various centrality measures exist, each emphasizing a different aspect of a node’s position within the network, such as degree centrality (the number of direct connections a node has), betweenness centrality (the number of times a node acts as a bridge along the shortest path between two other nodes), and eigenvector centrality (the sum of the centrality scores of all nodes that one node is connected to).
• Density : This is a measure of the proportion of possible connections in a network that are actual connections. A high density suggests that the network participants are highly interconnected.
• Clusters or Communities : These are groups of nodes that are more densely connected with each other than with the rest of the network.
• Structural Holes : These are gaps in the network where a node could potentially act as a bridge between two unconnected parts of the network.

Types of Social Network Analysis

Social Network Analysis can be broadly categorized based on the type of networks being analyzed, the level of analysis, and the methodologies employed. Here are a few ways to categorize SNA:

Whole Network Analysis

This type of analysis focuses on the structure and properties of the network as a whole. This might include measures of network cohesion, centralization, and density. It also looks at the overall distribution of relationships and identifies key groups or clusters within the network.

Ego Network Analysis

In this type of analysis, the focus is on a single actor (the ‘ego’) and their immediate network (the ‘alters’). It’s often used when interest is in the personal networks of individuals. Measures can include the size of the network, the composition of the network in terms of the types of ties and nodes, and measures of network density or diversity.

Two-mode (or Bipartite) Network Analysis

This type of SNA is used when there are two different types of nodes, and connections are only possible between nodes of different types (not within types). For example, authors and the books they write, or actors and the movies they appear in. In such a network, you can study the connections between nodes of one type, mediated by nodes of the other type.

Dynamic Network Analysis (DNA)

This is used to study how social networks evolve over time. This could involve studying how ties between actors develop or disappear, or how actors move around within the network. In addition to traditional network measures, DNA also considers measures that are dynamic in nature, such as change in centrality over time.

Semantic Network Analysis

This type of SNA focuses on the relationships between concepts or ideas, rather than individuals or organizations. For instance, semantic network analysis could map out how different scientific concepts are related to each other in the literature.

Social Media Network Analysis

A specialized form of SNA, this deals with the study of social relationships as expressed through social media platforms. It allows for the mapping and measuring of relationships and flows between people, groups, organizations, computers, URLs, and other connected information/knowledge entities.

Social Network Analysis Techniques

Social Network Analysis involves various techniques to understand the structure and patterns of relationships among actors (people, organizations, etc.) in a network. These techniques may be mathematical, visual, or computational, and often involve the use of specialized software. Here are several common SNA techniques:

Network Visualization

One of the most basic SNA techniques involves creating a visual representation of the network. This can help to reveal patterns and structures within the network that may not be immediately obvious from the raw data. There are various ways to create such visualizations, depending on the specifics of the network and the goals of the analysis. Software such as Gephi or Cytoscape can be used for network visualization.

Centrality Measures

These are techniques used to identify the most important nodes within a network. Various measures of centrality exist, each highlighting different aspects of a node’s position in the network. These include degree centrality (the number of connections a node has), betweenness centrality (how often a node appears on the shortest path between other nodes), closeness centrality (how quickly a node can reach all other nodes in the network), and eigenvector centrality (a measure of the influence of a node in a network).

Community Detection

Also known as clustering, this technique aims to identify groups of nodes that are more closely connected with each other than with the rest of the network. This can help to reveal sub-groups or communities within the network.

Structural Equivalence and Blockmodeling

Structural equivalence is a measure of how similarly two nodes are connected to the rest of the network. Nodes that are structurally equivalent often play similar roles in the network. Blockmodeling is a technique used to simplify a network by grouping together structurally equivalent nodes.

Dynamic Network Analysis

This involves studying how a network changes over time. This can help to reveal patterns of network evolution, including how relationships form and dissolve, how centrality measures change over time, and how communities evolve.

Network Correlation and Regression

These are statistical techniques used to identify and test for patterns within the network. For example, one might use these techniques to test whether nodes with certain characteristics are more likely to form connections with each other.

Social Network Analysis Tools

There are several tools available that can be used to conduct Social Network Analysis (SNA). These range from open-source software to commercial offerings, each with their own strengths and weaknesses. Here are a few examples:

• Gephi : Gephi is an open-source, interactive visualization and exploration platform for all kinds of networks and complex systems. It’s user-friendly and allows users to interactively manipulate the network visualization, perform network analysis, and export results in various formats.
• UCINet : UCINet is a comprehensive package for the analysis of social network data as well as other 1-mode and 2-mode data. It’s widely used in social science research.
• NetDraw : Often used in conjunction with UCINet, NetDraw is a free tool for visualizing networks. It supports the visualization of large networks and allows for various customization options.
• Pajek : Pajek is a program for the analysis and visualization of large networks. It’s an extensive tool, offering a range of complex network metrics, and is free for non-commercial use.
• NodeXL : NodeXL is a free, open-source template for Microsoft Excel that allows users to display and analyze network graphs. Its integration with Excel makes it user-friendly, particularly for those already familiar with Excel.
• Cytoscape : Originally designed for biological research, Cytoscape is now a popular open-source software platform for visualizing complex networks and integrating these with any type of attribute data.
• SocioViz : SocioViz is a social media analytics platform for Twitter data, focused on network analysis and visualization. It’s a powerful tool for researchers interested in online social networks.
• NetworkX : NetworkX is a Python package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks. It integrates well with other scientific Python tools like SciPy and Matplotlib.
• igraph : igraph is a library available in R, Python, and C for creating, manipulating, and analyzing networks. It’s highly efficient and can handle large networks.
• RSiena : RSiena is an R package dedicated to the statistical analysis of network data, with a particular focus on longitudinal social networks.

Social Network Analysis Examples

Social Network Analysis Examples are as follows:

• Public Health – COVID-19 Pandemic : During the COVID-19 pandemic, SNA was used to model the spread of the virus. The interactions between individuals were mapped as a network, helping identify super-spreader events and informing public health interventions.
• Business – Google’s “PageRank” Algorithm : Google’s PageRank algorithm, which determines the order of search engine results, is a type of SNA. It considers web pages as nodes and hyperlinks as connections, determining a page’s importance by looking at the number and quality of links to it.
• Sociology – Stanley Milgram’s “Small World” Experiment : This is one of the most famous social network experiments, where Milgram demonstrated that any two people in the United States are separated on average by only six acquaintances, leading to the phrase “six degrees of separation.”
• Online Social Networks – Facebook’s “People You May Know” Feature : Facebook uses SNA to suggest new friends. The platform analyzes your current network and suggests people you’re likely to know, typically friends of friends or people who share common networks.
• Criminal Network Analysis – Capture of Osama bin Laden : SNA was reportedly used in the operation to capture Osama bin Laden. By mapping the social connections of known associates, intelligence agencies were able to locate the Al-Qaeda leader.
• Academic Research – Collaboration Networks : SNA is used in scientometrics to analyze collaboration networks among researchers . For example, a study on co-authorship networks in scientific articles can reveal patterns of collaboration and the flow of information in different disciplines.

When to use Social Network Analysis

Social Network Analysis is a powerful tool for studying the relationships between entities (like people, organizations, or even concepts) and the overall structure of these relationships. Here are several situations when SNA might be particularly useful:

• Understanding Complex Systems : SNA is well-suited to studying complex, interconnected systems. If you’re interested in not just individual entities but also the relationships between them, SNA can provide valuable insights.
• Identifying Key Actors : SNA can help identify the most important entities in a network based on their position and connections. These might be influential people within a social network, critical servers in a computer network, or key scholars in a field of study.
• Studying Diffusion Processes : If you’re interested in how something (like information, behaviors, diseases) spreads through a network, SNA can be a valuable tool. It allows for the examination of diffusion pathways and identification of nodes that speed up or hinder diffusion.
• Detecting Communities : SNA can be used to identify clusters or communities within a network. These might be groups of friends within a social network, clusters of companies in a business network, or research clusters in scientific collaboration networks.
• Mapping Out Large Systems : In cases where you have a large system of many interconnected entities, SNA can provide a visual representation of the system, making it easier to understand and analyze.
• Investigating Structural Roles : If you’re interested in the roles individuals or entities play within their network, SNA offers methods to classify these roles based on the pattern of their relationships.

Purpose of Social Network Analysis

Social Network Analysis serves a wide range of purposes across different fields, given its versatile nature. Here are several key purposes:

• Understanding Network Structure : One of the key purposes of SNA is to understand the structure of relationships between actors within a network. This includes understanding how the network is organized, the distribution of connections, and the patterns of interaction.
• Identifying Key Actors or Nodes : SNA can identify crucial nodes within a network. These could be individuals with many connections, or nodes that serve as critical links between different parts of the network. In a business, for instance, such nodes might be key influencers or innovators.
• Detecting Subgroups or Communities : SNA can identify clusters or communities within a network, i.e., groups of nodes that are more connected to each other than to the rest of the network. This can be valuable in numerous contexts, from identifying communities in social media networks to detecting collaboration clusters in scientific networks.
• Analyzing Information or Disease Spread : In public health and communication studies, SNA is used to study the patterns and pathways of information or disease spread. Understanding these patterns can be critical for designing effective interventions or campaigns.
• Analyzing Social Capital : SNA can help understand an individual or group’s social capital – the resources they can access through their network relationships. This analysis can offer insights into power dynamics, access to resources, and inequality within a network.
• Studying Network Dynamics : SNA can examine how networks change over time. This could involve studying how relationships form or dissolve, how centrality measures change over time, or how communities evolve.
• Predicting Future Interactions : SNA can be used to predict future interactions or relationships within a network, which can be useful in a variety of settings such as recommender systems, predicting disease spread, or forecasting emerging trends in social media.

Applications of Social Network Analysis

Social Network Analysis has a wide range of applications across different disciplines due to its capacity to analyze relationships and interactions. Here are some common areas where it is applied:

• Public Health : SNA can be used to understand the spread of infectious diseases within a community or globally. It helps identify “super spreaders” and optimizes strategies for vaccination or containment.
• Business and Organizations : Companies use SNA to analyze communication and workflow patterns, enhance collaboration, boost efficiency, and detect key influencers within their organization. It can also be applied in understanding and leveraging informal networks within a business.
• Social Media Analysis : On platforms like Facebook, Twitter, or Instagram, SNA helps analyze user behavior, track information dissemination, identify influencers, detect communities, and develop recommendation systems.
• Criminal Justice : Law enforcement and intelligence agencies use SNA to understand the structure of criminal or terrorist networks, identify key figures, and predict future activities.
• Internet Infrastructure : SNA helps in mapping the internet, identifying critical nodes, and developing strategies for robustness against cyberattacks or outages.
• Marketing : In marketing, SNA can track the diffusion of advertising messages, identify influential consumers for targeted marketing, and understand consumer behavior and brand communities.
• Scientometrics : SNA is used in academic research to map co-authorship networks or citation networks. It can uncover patterns of collaboration and the flow of knowledge in scientific fields.
• Politics and Policy Making : SNA can help understand political alliances, lobby networks, or policy networks, which can be critical for strategic decision-making in politics.
• Ecology : In ecological studies, SNA can help understand the relationships between different species in an ecosystem, providing valuable insights into ecological dynamics.

Advantages of Social Network Analysis

Social Network Analysis offers several advantages when studying complex systems and relationships. Here are a few key advantages:

• Reveals Complex Relationships : SNA allows for the study of relationships between entities (be they people, organizations, computers, etc.) in a way that many other methodologies do not. It emphasizes the importance of these relationships and helps reveal complex interaction patterns.
• Identifies Key Players : SNA can identify the most influential or important nodes in a network, whether they are individuals within a social network, key servers in an internet network, or central scholars in an academic field.
• Unveils Network Structure and Communities : SNA can help visualize the overall structure of a network and can reveal communities or clusters of nodes within a network. This can provide valuable insights into the organization and division of a network.
• Tracks Changes Over Time : Dynamic SNA allows the study of networks over time. This can help to track changes in the network structure, the role of specific nodes, or the flow of information or resources through the network.
• Helps Predict Future Interactions : Based on the analysis of current and past relationships, SNA can be used to predict future interactions, which can be useful in many fields including public health, marketing, and national security.
• Aids in Designing Effective Strategies : The insights gained from SNA can be used to design targeted strategies, whether that’s intervening in the spread of misinformation online, designing a targeted marketing campaign, disrupting a criminal network, or managing collaboration in an organization.
• Versatility : SNA can be applied to a vast array of fields, from sociology to computer science, biology to business, making it a versatile tool.

Disadvantages of Social Network Analysis

While Social Network Analysis is a powerful tool with wide-ranging applications, it also has certain limitations and disadvantages that are important to consider:

• Data Collection Challenges : Collecting complete and accurate network data can be a major challenge. For larger networks, it may be nearly impossible to collect data on all relevant relationships. There’s also a risk of response bias, as people may forget, overlook, or misinterpret their relationships when providing data.
• Time and Resource Intensive : Collecting network data, especially from primary sources, can be extremely time-consuming and expensive. Additionally, analyzing network data can also require significant computational resources for larger networks.
• Complexity : SNA involves complex concepts and measures, which can be difficult to understand without specialized knowledge. This complexity can make it difficult to communicate findings to a non-technical audience.
• Privacy and Ethical Concerns : SNA often involves sensitive data about individuals’ relationships and interactions, raising important privacy and ethical concerns. It’s important to handle this data carefully to respect individuals’ privacy.
• Static Snapshots : Traditional SNA often provides a static snapshot of a network at a particular point in time, which may not capture the dynamic nature of social relationships. While dynamic SNA does exist, it adds additional complexity and data demands.
• Dependence on Quality of Data : The insights and conclusions drawn from SNA are only as good as the data used. Incomplete, inaccurate, or biased data can lead to misleading results.
• Difficulties in Establishing Causality : While SNA can reveal patterns and associations in network data, it can be difficult to establish causal relationships. For instance, do strong connections between two individuals lead to similar behavior, or does similar behavior lead to strong connections?
• Assumptions about Relationships : SNA often assumes that relationships are equally important, which might not always be the case. Different relationships might have different strengths or meanings, which can be challenging to represent in a network.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

You may also like

Diagnostic Analytics – Methods, Tools and...

Descriptive Analytics – Methods, Tools and...

What is Data Science? Components, Process and Tools

What is Big Data? Types, Tools and Examples

Sentiment Analysis – Tools, Techniques and...

Prescriptive Analytics – Techniques, Tools and...

ORIGINAL RESEARCH article

A network analysis of post-traumatic stress disorder symptoms and correlates during the covid-19 pandemic.

• 1 School of Psychology, Central China Normal University, Wuhan, China
• 2 Key Laboratory of Adolescent Cyberpsychology and Behavior, Ministry of Education, Wuhan, China
• 3 Key Laboratory of Human Development and Mental Health of Hubei Province, Wuhan, China

Background and Objective: The coronavirus disease 2019 (COVID-19) outbreak has been suggested as a collective trauma, which presents a continuing crisis. However, the specific post-traumatic implication of this crisis has not been adequately studied yet. The current study was aimed to ascertain the most central symptom and the strong connections between symptoms of post-traumatic stress disorder (PTSD). At the same time, exploring the relationship between covariates and the network of PTSD symptoms, by taking sex, anxiety, depression, suicidal ideation, quality of life, and social support as covariates, may help us to know the arise and maintenance of PTSD symptoms and give specified suggestions to people under the shadow of COVID-19.

Method: The Post-traumatic Stress Disorder Checklist for Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5), was used to assess the PTSD symptoms extent of 338 healthy participants over the past month. Networks were analyzed using state-of-the-art regularized partial correlation models. In addition, the centrality of the symptoms and the robustness of the results were analyzed.

Results: The network analysis revealed that the especially strong connections emerged between avoidance of thoughts and avoidance of reminders, hypervigilance and exaggerated startle response, intrusive thoughts and nightmares, flashbacks and emotional cue reactivity, and detachment and restricted affect. The most central symptoms were self-destructive/reckless behavior. Incorporation of covariates into the network revealed the strong connections path between self-destructive/reckless behavior and loss of interest and depression.

Conclusion: Self-destructive/reckless behavior was the most central symptom in the network of PTSD symptoms related to the COVID-19 pandemic, which as an important target of interfere may have great benefits.

Introduction

Coronavirus disease 2019 (COVID-19) presents one of the greatest global public health threats of the twenty first century. On March 11, 2020, the World Health Organization (WHO) declared the COVID-19 coronavirus outbreak a pandemic. In China, the government advised citizens into home quarantine and inhibited most public transportations on January 23, 2020. COVID-19 has impacted every aspect of society ( 1 ). It has not only caused physical health issues, the pandemic and the need for isolation have also increased psychological health problems, including post-traumatic stress disorder (PTSD), depression, anxiety, and widespread fear ( 2 , 3 ). Moreover, due to unprecedented levels of documentation and public exposure, COVID-19 may affect the majority of the population and cause vicarious trauma ( 4 ). The COVID-19 outbreak has been suggested as a collective trauma, which is a continuing crisis for everyone ( 5 – 7 ). However, the specific post-traumatic implication of this crisis has not been adequately studied yet. To prevent potential PTSD, it is necessary to investigate the characteristics of symptoms related to traumatic stress in people exposed to the COVID-19 crisis.

PTSD follows traumatic events and is characterized by symptoms of avoidance, intrusions, excessive arousal, and emotional numbing, etc ( 8 ). Previous studies on PTSD mostly adopted the reflective models based on the common cause hypothesis ( 9 , 10 ). According to these models, symptoms reflect an underlying latent construct (i.e., disorder), which means the symptom covariance is caused by the latent construct, and it is causally independent among the symptoms themselves ( 11 ). For example, based on this perspective, studies on the prevalence of PTSD during COVID-19 found that about 10% of the population meet the PTSD criteria, and subthreshold disturbances accounted for a large proportion of PTSD disturbance ( 6 , 12 – 15 ). Recently, McNally et al. ( 16 ) have proposed a causal system and suggested causal connections among PTSD symptoms that occur. For example, survivors who are exposed to trauma cues will likely be reactive and aroused, leading to avoidance behaviors. In addition, Ehlers and Clark ( 17 ) have assumed that individuals may have a negative bias in the evaluation of trauma and its outcomes after experiencing a traumatic event, and negative bias will cause avoidance of trauma cues, thereby increasing the sensitivity to threat and level of anxiety, leading to a vicious circle, which tend to maintain the PTSD symptoms. Empirical studies also showed that the factor structure of PTSD symptoms was varying in different traumatic experiences ( 18 – 20 ). Moreover, the relationships between PTSD symptoms and other psychological symptoms (e.g., anxiety, depression, and quality of life) ( 21 – 24 ), as well as the responses to treatment are changeable for different PTSD symptoms ( 25 ). However, neither the most central PTSD symptoms related to COVID-19 nor the related covariates were clear yet.

Network analysis has emerged as an approach involved in causal systems perspective. Specifically, network analysis is a methodology based on graph theory. Such methodology could be used to visualize the interaction between all observed variables, including psychopathology symptoms ( 26 ). The underlying hypothesis is that symptoms are interdependent, and a psychological disorder constitutes a network of symptoms that interact ( 11 , 27 , 28 ). Furthermore, network analysis enables computation of centrality that reveals the most important target of clinical interventions ( 9 ). Recently, network analysis has been applied to examine the constructs of mental disorders such as depression, schizophrenia, and anxiety disorders ( 29 – 32 ).

Network analysis has been used to identify the construct of PTSD, revealing that the factor structure of symptoms varied in different traumatic events. The studies have consistently found strong connections between hypervigilance and exaggerated startle response and between flashbacks and nightmares ( 16 , 33 – 37 ). However, there is no agreement on the most central symptoms yet. The following symptoms have been identified as central symptoms of PTSD: negative trauma-related emotions ( 33 ), feeling emotionally numb ( 34 ), intrusions and concentration deficits ( 35 ), intrusive recollections and flashbacks ( 36 ), feeling detached ( 27 ), hypervigilance ( 16 ), and emotional cue reactivity ( 37 ). The researchers attributed the discrepancy to the different traumatic events, including natural disasters, wars, accidents (e.g., car accidents), man-made disasters (e.g., abuse), etc. However, a cross-cultural study showed moderate to high correlations of network structure and centrality estimates between four trauma patient samples with different cultures and types and severity of trauma ( 38 ). COVID-19 has been suggested as a new type of mass trauma ( 5 ) or a collective trauma ( 7 ), which was different from trauma on an individual level. It is necessary to investigate the PTSD symptom network related to the COVID-19 pandemic and further examine the most central symptoms so as to develop more targeted interventions.

In addition, previous studies have revealed individual difference in the network of PTSD symptoms. For example, Armor et al. ( 33 ) included sex, age, anxiety, depression, suicidal ideation, mental and physical functioning, and quality of life in the PTSD symptom network and found a strong connection between self-destructive/reckless behavior and suicidal ideation. They also found associations between difficulty concentrating and anxiety and depression, as well as associations between quality of life and restricted affect and depression. The findings suggested considering depression, anxiety, and suicidal ideation when diagnosing and treating PTSD. In order to expand the PTSD symptom network, Birkeland and Heir ( 34 ) included sex, severity of exposure, and social support as covariates. The results showed that women had a stronger physiological cue activity compared to men and a correlation between low social support and difficulty sleeping. Cao et al. ( 36 ) emphasized the impact of sex and revealed sex differences in both global connectivity and individual symptoms' connectivity of PTSD symptom networks. These findings indicate that females and persons who receive less social support are relatively more vulnerable to PTSD when they are exposed to traumatic events.

Conclusively, network analysis reveals the interactions among symptoms and the relationships between symptoms and covariates. It is still unclear for the PTSD symptom network and the relationships between covariates and symptoms of the people who were exposed to the COVID-19 outbreak. Therefore, the present study aimed to investigate the network of PTSD symptoms and the most central symptoms on populations who were exposed to the COVID-19 outbreak to examine the role of covariates including sex, anxiety, depression, suicidal ideation, social support, and quality of life in the PTSD symptom network.

Participants

This study was conducted between April 4 and April 10, 2020, when the government ended the lockdown of Wuhan and the COVID-19 crisis was under control in China (April 8). Questionnaires were distributed online using a snowball sampling approach. Specifically, we posted advertisements that described the purpose of the study and the principle of voluntary participation on well-known social software (WeChat and Tencent QQ) in China. The participants recruited in the study voluntarily shared the advertisements to relatives and friends. We used online questionnaires to collect data through the Questionnaire Star platform. A total of 361 questionnaires were completed. A total of 338 (252 females) valid questionnaires were analyzed after deleting recurring responses. The subjects were paid 3 yuan after completing the survey.

The average age of participants was 25.76 years (SD = 9.61). Among them, 19.8% of the participants were in Hubei Province, among which 48.5% of them were in Wuhan, the hardest-hit area in China during the COVID-19 outbreak. Moreover, 67.9% of the participants had a bachelor's degree, and 20.3% had a master's degree or above. Additionally, most of the participants were unmarried (81.3%). Also, 64.6% of the participants were students, 28.9% had a stable job, and 6.5% were unemployed. In addition, 16.7% of the participants worked as a volunteer during the COVID-19 outbreak, and 0.3% had been infected with COVID-19. The studies involving human participants were reviewed and approved by the Ethic Institutional Review Board of Central China Normal University.

Post-traumatic Stress Disorder Symptoms

PTSD symptoms were assessed by the Post-traumatic Stress Disorder Checklist for Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5) (PCL-5) ( 39 , 40 ). The PCL-5 is a self-report measure and contains 20 items that correspond to the DSM-5 symptoms of PTSD. It measures the severity of PTSD symptoms over the last 1 month, rated on a 5-point Likert scale ranging from 0 (not at all) to 4 (extremely). To ensure that the PTSD symptoms we measured were related to the COVID-19 pandemic, we specified traumatic event as the COVID pandemic in the instructions. The Cronbach's alpha coefficient of PCL-5 was 0.94 in our study.

Depression and Anxiety Symptoms

Depression and anxiety symptoms were measured using Patient Health Questionnaire-4 (PHQ-4) ( 41 ), which is a self-assessment screening tool for depression and anxiety. The PHQ-4 consists of four items; the depression subscale includes two items and the anxiety subscale includes two items. The response options range from 0 (never) to 3 (nearly everyday). Each total score of the subscales indicates the severity of depression and anxiety, respectively, in which higher scores reflect greater severity of symptoms. In the present study, the Cronbach's alpha coefficient of depression subscale was 0.74, and the Cronbach's alpha coefficient of anxiety subscale was 0.81.

Suicidal Ideation

Suicidal ideation was assessed by the revised suicidal ideation subscale of PHQ-9 ( 42 ). The subscale contains two items, which evaluates passive and active suicidal ideation, respectively ( 43 ). Specifically, the items are “How often have you been bothered by the thoughts that you would be better off dead?” and “How often have you been bothered by the thoughts of hurting yourself?” over the last 2 weeks. The response options range from 0 (never) to 3 (nearly everyday). Higher summary scores indicate stronger suicidal ideation. The Cronbach's alpha coefficient of suicidal ideation subscale was 0.90 in our study.

Social Support

The Crisis Support Scale (CSS) ( 44 ) was used to measure the social support that the participants received during the COVID-19 outbreak. The CSS includes seven items that are answered on a 7-point Likert scale ranging from 1 (never) to 7 (always). Higher total scores reflect higher social support. The Cronbach's alpha coefficient of CSS was 0.82 in the present study.

Quality of Life

The quality of life was measured using the 12-item Short-Form Health Survey (SF-12) ( 45 ). The SF-12 has been widely used to evaluate the quality of life related to health, reflecting individual health status and impact of health status on daily life. The questionnaire contains two subscales including 12 items: physical health and mental health. The raw scores have been transformed into standard score (mean = 50, SD = 10) ( 46 ). The range of standardized score was 0 to 100. The quality of life was indicated by average score of the two subscales, and higher scores reflect better quality of life. In this study, the Cronbach's alpha coefficient of SF-12 was 0.80.

Data Analysis

We used SPSS 24.0 (IBM Corp., Armonk, USA) to analyze participant characteristics. Estimations of network, centrality, and robustness were carried out in the free statistical environment R, following the suggestion of the developers on network analysis ( 47 ).

Network Estimate and Visualization

Two networks were estimated and visualized using R-package qgraph ( 48 ). We build a network containing 20 PTSD symptoms. In addition, we included six covariates (sex, anxiety, depression, suicidal ideation, social support, and quality of life) in the PTSD symptom network. The network consists of nodes and edges. In this present study, symptoms and covariates are “nodes,” and the relationships between the nodes are “edges.” We estimated the network of partial correlation coefficients via Gaussian Graphical Model. That is, the edge between two nodes was weighted connection controlling for all other edges in the network. It can be understood as a partial correlation, representing conditional independence associations, in which the range of the weight is from −1 to 1 ( 49 ).

Specifically, we estimated all the association parameters among the nodes of the network using the cor_auto of R package qgraph. It estimates a large number of parameters (i.e., 190 pairwise association parameters in the network with 20 nodes, 325 pairwise association parameters in the network with 26 nodes) that may result in some false-positive connections. To minimize the false-positive connections, we set small edges to zero by applying a regularization method (EBOCglasso) that was revised from the least absolute shrinkage and selection operator ( 50 , 51 ). In addition, we calculated and visualized the networks using R package qgraph and bootnet. Nodes with stronger average associations were placed closer to the center of the graph via Fruchterman–Reingold algorithm ( 52 ). The green edges indicate positive associations, while the red edges represent negative associations. Furthermore, the thickness of the edges reflects the magnitude of the connection; that is, thicker edges indicate stronger connections.

Centrality Estimate

We calculated node centrality in the PTSD symptom network to identify the most central symptoms. Higher centrality indicates that the symptom has stronger connections with other symptoms ( 26 , 47 ). For each node, we estimated three commonly used indices of centrality: strength, closeness, and betweenness ( 53 ). Strength was calculated as the sum of edge weights of a node, reflecting direct connection strength of a node with other nodes in the network. Closeness was indexed by the inverse of the sum of distance from the node to all other nodes, indicating indirect connection strength of a node with other nodes in the network. The path between one node and the other node is shorter, the influence of this node on the other one is greater. Betweenness was assessed as the frequency that a node lies on the shortest path between two nodes, which indicated how central the node was when connecting all other nodes in the network.

In addition, expected influence (EI) indicates centrality by estimating the sum of the original score of each node ( 54 ), which was involved with the weight of connections as well as the direction of connections ( 55 ). Exploratively, we estimated one-step EI using R package bootnet ( 47 ) and compared it with the centrality index above. Higher EI represents higher centrality of a node ( 27 , 56 , 57 ).

Robustness Estimation and Testing for Significance

Estimation of robustness (i.e., accuracy and stability) of a psychopathology network is still a main challenge in network analysis. As suggested by Epskamp et al. ( 47 ), we used R package bootnet to assess the robustness of networks in our study. Bootstrapping of R package bootnet was used to test the robustness of edge weights and the robustness of centrality indices.

First, we calculated 95% confidence intervals for the edge weights and tested for differences in edge weights and centrality indices based on 1,000 bootstrap iterations at the alpha level of 0.05. Second, a node-dropping subsetting bootstrap technique and the correlation stability (CS) coefficient were applied to estimate the stability of centrality indices. That is, if the correlation between centrality values calculated from a subsample with participants missing and centrality values calculated from the complete data set is high (>0.7 by default), we would consider that the centrality metric is stable. The CS coefficient is an index for centrality stability, and the value should be more than 0.25, preferably higher than 0.5 ( 47 ).

We estimated the robustness of edge weights in both the PTSD symptom network and the network with covariates, while we only assessed the stability of centrality indices in the PTSD symptom network.

Sample Characteristics

The mean PCL-5 score was 12.90 (SD = 11.07). Also, 3.5% of the 338 participants reported a sum of PTSD symptoms over the PCL-5 cut point at 38 ( 58 ), 25.44% fulfilled two or more than two criteria of the B-E diagnosis criteria but with total PCL-5 scores of under 38 ( 59 ). Table 1 shows the means and standard deviations (SDs) of PTSD symptoms and covariates.

Table 1 . Means and standard deviations of post-traumatic stress disorder (PTSD) symptoms and covariates.

Post-traumatic Stress Disorder Symptom Network

Figure 1 shows the network structure of the 20 PTSD symptoms. Most of the connections between symptoms were positive. The bootstrap difference test indicated five associations significantly higher than at least half of the other edges: between avoidance of thoughts (C1) and avoidance of reminders (C2), hypervigilance (E3) and exaggerated startle response (E4), intrusive thoughts (B1) and nightmares (B2), flashbacks (B3) and emotional cue reactivity (B4), and detachment (D6) and restricted affect (D7) (shown in Supplementary Figure 1 in Supplemental Material).

Figure 1 . Estimated network of DSM-5 PTSD symptoms. B1, Intrusive thoughts; B2, Nightmares; B3, Flashbacks; B4, Emotional cue reactivity; B5, Physiological cue reactivity; C1, Avoidance of thoughts; C2, Avoidance of reminders; D1, Trauma-related amnesia; D2, Negative belief; D3, Blame of self or others; D4, Negative trauma-related emotions; D5, Loss of interest; D6, Detachment; D7, Restricted affect; E1, Irritability; E2, Self-destructive/reckless behavior; E3, Hypervigilance; E4, Exaggerated startle response; E5, Difficulty concentrating; E6, Sleep disturbance; PTSD, post-traumatic stress disorder; DSM-5, Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition.

The centrality indices (strength, closeness, and betweenness) are shown in Figure 2 . The three indices were significantly intercorrelated with each other (the correlation between strength and closeness was 0.59 ( p < 0.01), the correlation between strength and betweenness was 0.72 ( p < 0.01), and the correlation between closeness and betweenness was 0.81 ( p < 0.01). Recent studies have suggested that betweenness and closeness were unstable ( 56 , 57 ). Thus, we only focused on strength because of its reliability and the high correlations with other indices. The results showed that five symptoms [Self-destructive/reckless behavior (E2), Emotional cue reactivity (B4), Nightmares (B2), Restricted affect (D7), and Intrusive thoughts (B1)] had a high node strength. Significance testing indicated that only strength for Self-destructive/reckless behavior (E2) was significantly higher than other nodes (shown in Supplementary Figure 2 in Supplemental Material). Trauma-related amnesia (D1) and blame of self or others (D3) showed a relatively lower node strength.

Figure 2 . Centrality indices for the estimated network of DSM-5 PTSD symptoms. PTSD, post-traumatic stress disorder; DSM-5, Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition.

Additionally, the results showed that EI was significantly correlated with strength ( r = 0.80, p < 0.01). EI analysis revealed that the restricted affect (D7), Self-destructive/reckless behavior (E2), exaggerated startle response (E4), nightmares (B2), and avoidance of reminders (C2) were significantly intercorrelated with each other ( Supplementary Figure 3 ).

Post-traumatic Stress Disorder Network With Covariates

Figure 3 shows the network of PTSD symptoms including six covariates, namely, sex, anxiety, depression, suicidal ideation, social support, and quality of life. The results indicated strong connections between self-destructive/reckless behavior (E2) and suicidal ideation (0.83) and between loss of interest (D5) and depression (0.66). In addition, anxiety and depression were positively correlated (0.73), and suicidal ideation and quality of life were negatively associated (−0.61).

Figure 3 . Estimated network of DSM-5 PTSD symptoms including covariates. Anx, anxiety; Dep, depression; SI, suicidal ideation; SS, social support; SF, quality of life; PTSD, post-traumatic stress disorder; DSM-5, Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition.

Robustness of Networks

The estimated robustness (i.e., stability and accuracy) of 20 PTSD symptom network was presented in Figure 4A . The estimated robustness of PTSD symptom network with covariates (26 nodes) was shown in Figure 4B . The results showed that 95% confidence intervals for the edge weights were mostly overlapping in both networks. The bootstrap testing for the edge weights indicated that the estimation of the PTSD symptom network and the significance were accurate in both networks.

Figure 4 . Robustness of networks. (A) Bootstrap 95% confidence intervals for estimated edge weights in 20 PTSD symptom network. (B) Bootstrap 95% confidence intervals for estimated edge weights in PTSD symptom network with covariates. Red line presents the edge weights. The 95% confidence intervals are presented by the gray area. PTSD, post-traumatic stress disorder.

Figure 5 shows the estimated stability of the centrality indices for the 20 PTSD symptom network via node-dropping bootstrap technique. The results indicated a CS coefficient of 0.28 for strength.

Figure 5 . The average correlation between bootstrap centrality indices of networks sampled with node-dropping and network of the DSM-5 PTSD symptoms. PTSD, post-traumatic stress disorder; DSM-5, Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition.

The present study investigated the network of PTSD symptoms on people who were exposed to the COVID-19 outbreak. Specifically, we estimated and tested the accuracy and stability of two networks. One network contained 20 PTSD symptoms, and the other one included the 20 PTSD symptoms as well as six covariates. We will discuss the connections between the PTSD symptoms and the most central symptoms. We then discuss the relationships between the PTSD symptoms and the covariates.

The results showed strong connections between avoidance of thoughts (C1) and avoidance of reminders (C2), between hypervigilance (E3) and exaggerated startle response (E4), between intrusive thoughts (B1) and nightmares (B2), between flashbacks (B3) and emotional cue reactivity (B4), and between detachment (D6) and restricted affect (D7) in the network of PTSD symptoms related to the COVID-19 pandemic. It suggested that the most central symptom was self-destructive/reckless behavior (E2).

In the 20 PTSD symptom network, the strong connections between hypervigilance and exaggerated startle response and between intrusive thoughts and nightmares were consistent with previous studies ( 16 , 27 , 33 – 35 , 37 ). The strong connection between hypervigilance and exaggerated startle response indicated that the two symptoms affect each other through a feedback loop ( 16 ). It was supported by the Sensitization Model of PTSD. According to this model, survivors may become sensitive to the threat and show an exaggerated startle response after exposure to traumatic occurrences ( 60 ). Similarly, the strong connection between intrusive thoughts and nightmares indicated a loop in which intrusive thoughts about the traumatic event increase the possibility of nightmares associated with trauma, and in turn, the nightmares may make traumatic recollections more intrusive ( 34 ). In addition, the strong connection between detachment and restricted affect was also consistent with previous studies ( 16 , 33 , 35 , 36 , 38 ). This finding reflected that individuals with PTSD symptoms may regulate their emotions by disengaging from their emotions rather than engaging in the emotions. As a result, they may not only disengage from negative emotions related to trauma but also disengage from positive emotions after trauma ( 61 , 62 ).

Trauma-related amnesia showed the lowest node strength in the network of DSM-5 PTSD symptoms. This finding was compatible with previous findings of PTSD network analysis ( 16 , 33 , 34 , 37 ). Trauma-related amnesia has been suggested to be less useful in PTSD diagnosis ( 63 , 64 ). Furthermore, trauma-related amnesia showed a very weak factor loading in confirmatory factor analysis ( 65 ). It seems that PTSD associated with vivid traumatic memories rather than trauma-related amnesia ( 66 ). These findings suggested that trauma-related amnesia might not be a central symptom of PTSD. Moreover, when we excluded “amnesia” from the network analysis, the structure was hardly influenced (see Supplementary Materials for more details).

The finding of strong connection between avoidance of thoughts and avoidance of reminders conflicted with previous studies in which there was no strong connection. This incongruence may be partly the result of different types of trauma ( 18 ). Similarly, network analysis for depression also found different connections among symptoms due to different life events ( 67 , 68 ). The different intervals between traumatic event and conducting studies may also have contributed to this discrepancy. We conducted the investigation around 1 month after COVID-19 was controlled in China, while previous studies performed the studies much later after trauma than this present study ( 16 , 33 – 35 , 37 ).

Additionally, the strong connections among symptoms found in this study suggested that fear-conditioning models and dysphoric response might be central to the development of PTSD. That is, physiological and emotional responses to trauma cues and intrusive memories may lead to thoughts about traumatic events and avoidance of trauma cues ( 17 ), and intrusiveness and avoidance increase the sensitivity of perceived threats ( 35 , 69 ), as suggested in the fear-conditioning models ( 35 , 70 , 71 ). Subsequently, increased sensitivity of threats eventually results in dysphoric responses such as hypervigilance and exaggerated startle responses ( 17 ). However, whether the development of PTSD symptoms in the context of the COVID-19 outbreak is compatible with these models or not still needs to be tested in longitudinal studies ( 69 , 72 ).

In terms of the most central symptom, this study found that self-destructive/reckless behavior was at the center of the PTSD symptom network. The centrality analysis revealed that the strength of self-destructive/reckless behavior was significantly higher than that of other symptoms, while there was no significant difference of node strength between all the other symptoms. Therefore, self-destructive/reckless behavior might have the greatest clinical significance for the diagnosis of PTSD related to the COVID-19 pandemic. This symptom reflected high symptomatic burden and need for treatment. It is necessary to further investigate the factors that influence this symptom so as to develop more targeted interventions. However, this finding contrasted with most previous studies ( 16 , 33 , 35 ), which found self-destructive/reckless behavior to have only moderate centrality. This discrepancy may partly result from different types of trauma and different time points of investigating, as mentioned before. Additionally, different PTSD diagnostic criteria may also have contributed to this difference. For example, in some studies, the PTSD symptom networks were based on DSM-4 ( 16 , 34 , 35 , 38 ), in which self-destructive/reckless behavior was not included as one of the PTSD symptoms.

The findings of the strongly connected symptoms and core symptom in this study have important implications for PTSD symptoms associated with the COVID-19 pandemic. The alleviation of these symptoms may benefit for reducing other symptoms ( 73 – 75 ). However, some studies failed to support this statement ( 76 ). A recent study found no difference between central symptoms and other symptoms in terms of their influences on symptom network ( 77 ). In addition, the centrality measurement is unable to reveal the direction of correlations between central nodes and other symptoms. Thus, some researchers suggested the most different symptoms as effective treatment targets ( 78 ). Moreover, the present study was conducted on healthy populations. Therefore, further longitudinal studies are needed to test directly on populations whether the identified strong connections and central symptom in this study can provide a viable treatment in psychotherapy.

Post-traumatic Stress Disorder Symptom Network With Covariates

To extend the network of 20 PTSD symptoms, we included six clinically relevant covariates in the network. The strong connection between self-destructive/reckless behavior and suicidal ideation agreed with previous research, which revealed that self-destructive/reckless behaviors predicted suicidal ideation ( 33 , 79 ). Moreover, PTSD itself was highly associated with suicidal thoughts ( 80 ). Self-destructive/reckless behavior may be a risk factor for suicide, and clinicians should pay more attention to trauma survivors with increased self-destructive behaviors. In addition, the results showed a strong association between loss of interest and depression. A recent study revealed that loss of interest was one of the hub symptoms within a network of PTSD and severe depression ( 81 ). The hub symptoms serve as bridges between disorders, increasing risk for comorbidity and severity of comorbidity. Additionally, it was unsurprising to find a strong connection among covariates between depression and anxiety symptoms. These two symptoms were frequently reported to be interrelated in previous network studies, and depression and anxiety are common comorbidities ( 82 , 83 ). Therefore, it is necessary to consider depression and anxiety in the future studies of PTSD related to COVID-19.

In this present study, there was no impact of sex on the PTSD symptom network. This different finding from previous studies ( 36 ) might indicate that the impact of sex is on the overall connections of symptom network. Alternatively, this difference might due to our sample in which the number of females was much more than that of males. Interestingly, previous research has found that females were more vulnerable to PTSD than males ( 84 , 85 ), while COVID-19-related studies found the opposite pattern ( 13 , 15 ). Additional research that recruit equal female and male participants is necessary to investigate the effect of sex on the PTSD symptom network associated with COVID-19.

Consistent with previous studies, the PTSD symptom network has hardly changed when including covariates. It seems that the network of PTSD symptoms was relatively stable. However, it might also be due to the low scores of these variables in this study. More studies with larger samples are needed to test the effect of covariates on the PTSD symptom network.

In summary, the network analysis offers new insights into the interactions between PTSD symptoms themselves and other clinical conditions. The results had significant implications for understanding and intervention of PTSD related to the COVID-19 pandemic. Additionally, the sample set in this study included not only the participants who fulfilled the clinical diagnosis but also those who have not yet met clinical criteria. Previous studies have revealed that it is different between networks constructed based on clinical samples and non-clinical samples ( 86 ). Therefore, it is not enough to translate these findings into clinical practice. However, it is noteworthy that the individual difference of response to the COVID-19 outbreak is also clinically informative. COVID-19 is a threatening disease for human beings. It is unpredictable and need for distance and isolation. Moreover, the peri-traumatic phase of COVID-19 may be rather long ( 5 ). Therefore, it is important to help individuals who have a pathological burden but do not meet the PTSD diagnostic criteria to manage fears and worries and to develop coping skills for dealing with the ongoing threat.

Limitations and Future Research Directions

Several limitations of this study need to be considered. First, this study collected cross-sectional data, which cannot identify causality between PTSD symptoms. As a result, it was not clear whether the most central symptom caused other symptoms or the other way around—or both. Therefore, future research that uses a longitudinal design is needed. Second, most of samples were college students (64.6%). They were under academic stress and exposed to relatively more social media, leading to serious vicarious trauma ( 87 , 88 ). Furthermore, most of the samples were female. The findings in this study may be limitedly applied to young female populations. Therefore, these results require careful interpretation and translation into clinical practice. The robustness analyses revealed moderate instability, especially for the estimation of centrality parameters. The low stability of the network may be due to the small sample. Future studies with larger and sex-balanced samples are needed to improve the stability of the COVID-19-related PTSD symptom network. Third, the participants in this study were from different regions in China, where the severities of the COVID-19 pandemic were various. Consequently, the different severities of the COVID-19 outbreak may result in different symptoms and symptom networks. It is especially necessary to investigate the network of PTSD symptoms in the hard-hit regions by COVID-19 in the future. In addition, we have not checked if the participants had a PTSD history, which might interfere with the findings of PTSD symptom network ( 89 ). Fourth, this study used self-reported data, which limited objectivity and reliability ( 90 ). Future studies need to evaluate the PTSD symptom network more correctly through structured clinical interviews. It may be able to identify PTSD symptoms that are specific to the COVID-19 crisis. In addition, it is necessary to incorporate physiological and behavioral data to reveal the automatic processes that maintain PTSD symptoms in future research.

The present study is, to our knowledge, the first to perform a network analysis of PTSD symptoms related to the COVID-19 outbreak. The results showed strong connections between avoidance of thoughts and avoidance of reminders, between hypervigilance and exaggerated startle response, between intrusive thoughts and nightmares, between flashbacks and emotional cue reactivity, and between detachment and restricted affect in the network of PTSD symptoms related to the COVID-19 pandemic. The most central symptom was self-destructive/reckless behavior. These results had significant implications for understanding and intervention of PTSD related to the COVID-19 pandemic. We emphasize the self-destructive/reckless behavior as an important target in the treatment of PTSD, which may facilitate relief of most PTSD symptoms.

Data Availability Statement

All datasets generated for this study are included in the article/ Supplementary Material .

Ethics Statement

The studies involving human participants were reviewed and approved by the Ethic Institutional Review Board of Central China Normal University. The ethics committee waived the requirement of written informed consent for participation.

Author Contributions

All authors reviewed drafts of the paper. WJ: performed the experiments, wrote-original draft, and prepared figures and tables. ZR: designed the experiments and project administration. LY: conceptualization, methodology, and designed the experiments. YT: wrote-review and editing. CS: contributed reagents, materials, analysis tools. All authors contributed to the article and approved the submitted version.

Self-determined research funds of Central China Normal University, from the colleges' basic research and operation of Ministry of Education of China (grant no. CCNU20TD001). Key Program of Institute of Wuhan Studies of Jianghan University (grant no. IWHS20201007).

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fpsyt.2020.568037/full#supplementary-material

1. Boyraz G, Legros DN. Coronavirus disease (COVID-19) and traumatic stress: probable risk factors and correlates of posttraumatic stress disorder. J Loss Trauma. (2020) 25:1–20. doi: 10.1080/15325024.2020.1763556

CrossRef Full Text | Google Scholar

2. Mak IWC, Chu CM, Pan PC, Yiu MGC, Ho SC, Chan VL. Risk factors for chronic post-traumatic stress disorder (PTSD) in SARS survivors. Gen Hosp Psychiatry. (2010) 32:590–8. doi: 10.1016/j.genhosppsych.2010.07.007

PubMed Abstract | CrossRef Full Text | Google Scholar

3. Liang L, Ren H, Cao R, Hu Y, Qin Z, Li C, et al. The effect of COVID-19 on youth mental health. Psychiatr Q. (2020) 91:841–52. doi: 10.1007/s11126-020-09744-3

4. Li Z, Ge J, Yang M, Feng J, Yang C. Vicarious traumatization in the general public, members, and non-members of medical teams aiding in COVID-19 control. Brain Behav Immun. (2020) 88:916–9. doi: 10.1016/j.bbi.2020.03.007

5. Horesh D, Brown AD. Traumatic stress in the age of COVID-19 A call to close critical gaps and adapt to new realities. Psychol Trauma. (2020) 4:331–5. doi: 10.1037/tra0000592

6. Tang W, Hu T, Hu B, Jin C, Xu J. Prevalence and correlates of PTSD and depressive symptoms one month after the outbreak of the COVID-19 epidemic in a sample of home-quarantined Chinese university students. J Affect Disord. (2020) 274:1–7. doi: 10.1016/j.jad.2020.05.009

7. Venkateswaran KD, Hauser CT. Living with PTSD amid a global pandemic. Psychol Trauma. (2020) 12:S71–2. doi: 10.1037/tra0000857

8. Deja M, Denke C, Weber-Carstens S, Schröder J, Pille CE, Hokema F, et al. Social support during intensive care unit stay might improve mental impairment and consequently health-related quality of life in survivors of severe acute respiratory distress syndrome. Critical Care. (2006) 5:R147. doi: 10.1186/cc5070

9. Fried EI. Problematic assumptions have slowed down depression research: why symptoms, not syndromes are the way forward. Front Psychol. (2015) 6:309. doi: 10.3389/fpsyg.2015.00309

10. Schmittmann VD, Cramer AOJ, Waldorp LJ, Epskamp S, Kievit RA, Borsboom D. Deconstructing the construct: a network perspective on psychological phenomena. New Ideas Psychol. (2013) 31:43–53. doi: 10.1016/j.newideapsych.2011.02.007

11. Hofmann SG, Curtiss J, McNally RJ. A complex network perspective on clinical science. Perspect Psychol Sci. (2016) 11:597–605. doi: 10.1177/1745691616639283

12. Kang L, Ma S, Chen M, Yang J, Wang Y, Li R, et al. Impact on mental health and perceptions of psychological care among medical and nursing staff in Wuhan during the 2019 novel coronavirus disease outbreak: a cross-sectional study. Brain Behav Immun. (2020) 87:11–7. doi: 10.1016/j.bbi.2020.03.028

13. Liu N, Zhang F, Wei C, Jia Y, Shang Z, Sun L, et al. Prevalence and predictors of PTSS during COVID-19 outbreak in China hardest-hit areas: sex differences matter. Psychiatry Res. (2020) 287:112921. doi: 10.1016/j.psychres.2020.112921

14. Zhao Y, An Y, Tan X, Li X. Mental health and its influencing factors among self-isolating ordinary citizens during the beginning epidemic of COVID-19. J Loss Trauma. (2020) 25:1–14. doi: 10.1080/15325024.2020.1761592

15. Liang L, Gao T, Ren H, Cao R, Qin Z, Hu Y, et al. Post-traumatic stress disorder and psychological distress in Chinese youths following the COVID-19 emergency. J Health Psychol. (2020) 25:1164–75. doi: 10.1177/1359105320937057

16. McNally RJ, Robinaugh DJ, Wu GWY, Wang L, Deserno MK, Borsboom D. Mental disorders as causal systems: a network approach to posttraumatic stress disorder. Clin Psychol Sci. (2015) 3:836–49. doi: 10.1177/2167702614553230

17. Ehlers A, Clark DM. A cognitive model of posttraumatic stress disorder. Behav Res Ther. (2000) 38:319–45. doi: 10.1016/S0005-7967(99)00123-0

18. Armour C, Shevlin M. Testing the dimensionality of PTSD and the specificity of the dysphoria factor. J Loss Trauma. (2009) 15:11–27. doi: 10.1080/15325020903373110

19. Liu S, Wang L, Cao C, Zhang J. The factor structure of posttraumatic stress disorder symptoms in patients with traumatic spinal cord injuries. Arch Psychiatr Nurs . (2014) 28:301–4. doi: 10.1016/j.apnu.2014.05.008

20. Wang L, Zhang L, Armour C, Cao C, Qing Y, Zhang J, et al. Assessing the underlying dimensionality of DSM-5 PTSD symptoms in Chinese adolescents surviving the 2008 Wenchuan earthquake. J Anxiety Disord . (2015) 31:90–7. doi: 10.1016/j.janxdis.2015.02.006

21. Contractor AA, Durham TA, Brennan JA, Armour C, Wutrick HR, Christopher Frueh B, et al. DSM-5 PTSD's symptom dimensions and relations with major depression's symptom dimensions in a primary care sample. Psychiatry Res. (2014) 215:146–53. doi: 10.1016/j.psychres.2013.10.015

22. Giacco D, Matanov A, Priebe S. Symptoms and subjective quality of life in post-traumatic stress disorder: a longitudinal study. PLoS ONE. (2013) 8:e60991. doi: 10.1371/journal.pone.0060991

23. Li G, Wang L, Cao C, Fang R, Liu P, Luo S, et al. DSM-5 posttraumatic stress symptom dimensions and health-related quality of life among Chinese earthquake survivors. Eur J Psychotraumatol. (2018) 9:146871. doi: 10.1080/20008198.2018.1468710

24. Pietrzak RH, Tsai J, Armour C, Mota N, Harpaz-Rotem I, Southwick SM. Functional significance of a novel 7-factor model of DSM-5 PTSD symptoms: results from the national health and resilience in veterans study. J Affect Disord. (2015) 174:522–6. doi: 10.1016/j.jad.2014.12.007

25. Asmundson GJG, Stapleton JA, Taylor S. Are avoidance and numbing distinct PTSD symptom clusters? J Trauma Stress. (2004) 17:467–75. doi: 10.1007/s10960-004-5795-7

26. Borsboom D, Cramer AOJ. Network analysis: an integrative approach to the structure of psychopathology. Annu Rev Clin Psychol . (2013) 9:91–121. doi: 10.1146/annurev-clinpsy-050212-185608

27. McNally RJ. Can network analysis transform psychopathology? Behav Res Ther. (2016) 86:95–104. doi: 10.1016/j.brat.2016.06.006

28. Nuijten MB, Deserno MK, Cramer AOJ, Borsboom D. Mental disorders as complex networks: an introduction and overview of a network approach to psychopathology. Clin Neuropsychiatry. (2016) 13:68–76. Available online at: https://www.researchgate.net/publication/311469708

Google Scholar

29. Beard C, Millner AJ, Forgeard MJC, Fried EI, Hsu KJ, Treadway MT, et al. Network analysis of depression and anxiety symptom relationships in a psychiatric sample. Psychol Med. (2016) 46:3359–69. doi: 10.1017/S0033291716002300

30. Fried EI, Epskamp S, Nesse RM, Tuerlinckx F, Borsboom D. What are 'good' depression symptoms comparing the centrality of DSM and non-DSM symptoms of depression in a network analysis. J Affect Disord. (2016) 189:314–20. doi: 10.1016/j.jad.2015.09.005

31. Fried EI, van Borkulo CD, Cramer AOJ, Boschloo L, Schoevers RA, Borsboom D. Mental disorders as networks of problems: a review of recent insights. Soc Psychiatry Psychiatr Epidemiol. (2016) 52:1–10. doi: 10.1007/s00127-016-1319-z

32. Levine SZ, Leucht S. Identifying a system of predominant negative symptoms: network analysis of three randomized clinical trials. Schizophr Res . (2016) 178:17–22. doi: 10.1016/j.schres.2016.09.002

33. Armour C, Fried EI, Deserno MK, Tsai J, Pietrzak RH. A network analysis of DSM-5 posttraumatic stress disorder symptoms and correlates in U.S. military veterans. J Anxiety Disord. (2017) 45:49–59. doi: 10.1016/j.janxdis.2016.11.008

34. Birkeland MS, Heir T. Making connections: exploring the centrality of posttraumatic stress symptoms and covariates after a terrorist attack. Eur J Psychotraumatol. (2017) 8:1333387. doi: 10.1080/20008198.2017.1333387

35. Bryant RA, Creamer M, O'Donnell M, Forbes D, McFarlane AC, Silove D, et al. Acute and chronic posttraumatic stress symptoms in the emergence of posttraumatic stress disorder. JAMA Psychiatry. (2017) 74:135. doi: 10.1001/jamapsychiatry.2016.3470

36. Cao X, Wang L, Cao C, Fang R, Chen C, Hall BJ, et al. Sex differences in global and local connectivity of adolescent posttraumatic stress disorder symptoms. J Child Psychol Psychiatry. (2018) 60:216–24. doi: 10.1111/jcpp.12963

37. Spiller TR, Schick M, Schnyder U, Bryant RA, Nickerson A, Morina N. Symptoms of posttraumatic stress disorder in a clinical sample of refugees: a network analysis. Eur J Psychotraumatol. (2017) 8:1318032. doi: 10.1080/20008198.2017.1318032

38. Fried EI, Eidhof MB, Palic S, Costantini G, Dijk HMH, Bockting CLH, et al. Replicability and generalizability of PTSD networks: a crosscultural multisite study of PTSD symptoms in four trauma patient samples. Clin Psychol Sci . (2018) 6:335–51. doi: 10.1177/2167702617745092

39. Weathers FW, Blake DD, Schnurr PP, Kaloupek DG, Marx BP, Keane TM. The Clinician-Administered PTSD Scale for DSM-5 (CAPS-5) . National Center for PTSD (2013). Available online at: www.ptsd.va.gov (accessed April 1, 2020).

40. Weathers FW, Litz BT, Keane TM, Palmieri PA, Marx BP, Schnurr PP. The PTSD Checklist for DSM-5 (PCL-5) . National Center for PTSD (2013). Available online at: www.ptsd.va.gov (accessed April 1, 2020).

41. Kroenke K, Spitzer RL, Williams JB, Löwe B. An ultra-brief screening scale for anxiety and depression the PHQ−4. Psychosomatics. (2009) 50:613–21. doi: 10.1016/S0033-3182(09)70864-3

42. Kroenke K, Spitzer RL, Williams JBW. The PHQ-15: validity of a new measure for evaluating the severity of somatic symptoms. Psychosom Med . (2002) 64:258–66. doi: 10.1097/00006842-200203000-00008

43. Thompson R, Henkel V, Coyne JC. Suicidal ideation in primary care: ask a vague question, get a confusing answer. Psychosom Med. (2004) 66:455–6. doi: 10.1097/00006842-200405000-00026

44. Joseph S, Andrews B, Williams R, Yule W. Crisis support and psychiatric symptomatology in adult survivors of the Jupiter cruise ship disaster. Br J Clinical Psychol. (1992) 31:63–73. doi: 10.1111/j.2044-8260.1992.tb00968.x

45. Ware JE, Kosinski M, Keller SD. A 12-item short-form health survey construction of scales and preliminary tests of reliability and validity. Med Care. (1996) 3:220–33. doi: 10.1097/00005650-199603000-00003

46. Ware JE, Kosinski M, Turner-Bowker DM, Gandek B. How to Score Version 2 of the SF-12 Health Survey (With a Supplement Documenting Version 1) . Quality Metric Incorporated (2002).

47. Epskamp S, Borsboom D, Fried EI. Estimating psychological networks and their stability: a tutorial paper. Behav Res Methods. (2017) 50:195–212. doi: 10.3758/s13428-017-0862-1

48. Epskamp S, Cramer AO, Waldorp LJ, Schmittmann VD, Borsboom D. qgraph: network visualizations of relationships in psychometric data. J Stat Softw. (2012) 48:1–18. doi: 10.18637/jss.v048.i04

49. Epskamp S, Fried EI. A primer on estimating regularized psychological networks. arXiv. (2016) arXiv Preprint:160701367. doi: 10.1037/met0000167

CrossRef Full Text

50. Tibshirani R. Regression shrinkage and selection via the lasso. J R Stat Soc B. (1996) 58:267–88. doi: 10.1111/j.2517-6161.1996.tb02080.x

51. Van Borkulo CD, Borsboom D, Epskamp S, Blanken TF, Boschloo L, Schoevers RA, et al. A new method for constructing networks from binary data. Sci Rep. (2014) 4:5918. doi: 10.1038/srep05918

52. Fruchterman TMJ, Reingold EM. Graph drawing by force-directed placement. Softw Pract Exp. (1991) 21:1129–64. doi: 10.1002/spe.4380211102

53. Opsahl T, Agneessens F, Skvoretz J. Node centrality in weighted networks: generalizing degree and shortest paths. Soc Netw. (2010) 32:245–51. doi: 10.1016/j.socnet.2010.03.006

54. Wang SB, Jones PJ, Dreier M, Elliott H, Grilo CM. Core psychopathology of treatment-seeking patients with binge-eating disorder: a network analysis investigation. Psychol Med. (2018) 49:1–6. doi: 10.1017/S0033291718002702

55. Heeren A, Jones PJ, Mcnally RJ. Mapping network connectivity among symptoms of social anxiety and comorbid depression in people with social anxiety disorder. J Affect Disord. (2018) 228:75–82. doi: 10.1016/j.jad.2017.12.003

56. Bringmann LF, Elmer T, Epskamp S, Krause RW, Snippe E. What do centrality measures measure in psychological networks? J Abnorm Psychol. (2019) 128:892–903. doi: 10.1037/abn0000446

57. Hallquist MN, Wright AGC, Molenaar PCM. Problems with centrality measures in psychopathology symptom networks: why network psychometrics cannot escape psychometric theory. Multivariate Behav Res. (2019) 12:1–25. doi: 10.1080/00273171.2019.1640103

58. Hoge CW, Riviere LA, Wilk JE, Herrell RK, Weathers FW. The prevalence of post-traumatic stress disorder (PTSD) in US combat soldiers: a head-to-head comparison of DSM-5 versus DSM-IV-TR symptom criteria with the PTSD checklist. Lancet Psychiatry. (2014) 1:269–77. doi: 10.1016/S2215-0366(14)70235-4

59. McLaughlin KA, Koenen KC, Friedman MJ, Ruscio AM, Karam EG, Shahly V, et al. Subthreshold posttraumatic stress disorder in the world health organization world mental health (WMH) surveys. Biol Psychiatry. (2014) 77:375–84. doi: 10.1016/j.biopsych.2014.03.028

60. Stam R. PTSD and stress sensitisation: a tale of brain and body: part 1: human studies. Neurosci Biobehav Rev . (2007) 31:530–57. doi: 10.1016/j.neubiorev.2006.11.010

61. Litz BT, Orsillo SM, Kaloupek D, Weathers F. Emotional processing in posttraumatic stress disorder. J Abnorm Psychol . (2000) 109:26–39. doi: 10.1037/0021-843X.109.1.26

62. Shepherd L, Wild J. Emotion regulation, physiological arousal and PTSD symptoms in trauma-exposed individuals. J Behav Ther Exp Psychiatry. (2014) 45:360–7. doi: 10.1016/j.jbtep.2014.03.002

63. Geraerts E, McNally RJ. Forgetting unwanted memories: directed forgetting and thought suppression methods. Acta Psychol. (2008) 127:614–22. doi: 10.1016/j.actpsy.2007.11.003

64. Rubin DC, Berntsen D, Bohni MK. A memory-based model of posttraumatic stress disorder: evaluating basic assumptions underlying the PTSD diagnosis. Psychol Rev . (2008) 115:985–1011. doi: 10.1037/a0013397

65. Armour CM, Ullerová J, Elhai JD. A systematic literature review of PTSD's latent structure in the diagnostic and statistical manual of mental disorders: DSM-IV to DSM-5. Clin Psychol Rev . (2016) 44:60–74. doi: 10.1016/j.cpr.2015.12.003

66. Porter S, Peace KA. The scars of memory: a prospective, longitudinal investigation of the consistency of traumatic and positive emotional memories in adulthood. Psychol Sci . (2007) 18:435–41. doi: 10.1111/j.1467-9280.2007.01918.x

67. Cramer AOJ, Borsboom D, Aggen SH, Kendler KS. The pathoplasticity of dysphoric episodes: differential impact of stressful life events on the pattern of depressive symptom inter-correlations. Psychol Med. (2011) 42:957–65. doi: 10.1017/S003329171100211X

68. Fried EI, Bockting C, Arjadi R, Borsboom D, Amshoff M, Cramer AOJ, et al. From loss to loneliness: the relationship between bereavement and depressive symptoms. J Abnorm Psychol . (2015) 2:256–65. doi: 10.1037/abn0000028

69. Price M, Legrand AC, Brier ZMF, Gratton J, Skalka C. The short-term dynamics of posttraumatic stress disorder symptoms during the acute posttrauma period. Depress Anxiety. (2019) 37:313–20. doi: 10.1002/da.22976

70. Zoellner LA, Rothbaum BO, Feeny NC. PTSD not an anxiety disorder? DSM committee proposal turns back the hands of time. Depress Anxiety. (2011) 28:853–6. doi: 10.1002/da.20899

71. Hoge CW, Yehuda R, Castro CA, Mcfarlane AC, Vermetten E, Jetly R, et al. Unintended consequences of changing the definition of posttraumatic stress disorder in DSM-5: critique and call for action. JAMA Psychiatry. (2016) 73:750–2. doi: 10.1001/jamapsychiatry.2016.0647

72. Greene T, Gelkopf M, Epskamp S, Fried E. Dynamic networks of PTSD symptoms during conflict. Psychol Med . (2018) 48:2409–17. doi: 10.1017/S0033291718000351

73. Robinaugh DJ, Millner AJ, Mcnally RJ. Identifying highly influential nodes in the complicated grief network. J Abnorm Psychol. (2016) 125:747–57. doi: 10.1037/abn0000181

74. Rodebaugh TL, Tonge NA, Piccirillo ML, Fried E, Horenstein A, Morrison AS, et al. Does centrality in a cross-sectional network suggest intervention targets for social anxiety disorder? J Consult Clin Psychol. (2018) 86:831–44. doi: 10.1037/ccp0000336

75. Haag C, Robinaugh DJ, Ehlers A, Kleim B. Understanding the emergence of chronic posttraumatic stress disorder through acute stress symptom networks. JAMA Psychiatry . (2017) 6:649–50. doi: 10.1001/jamapsychiatry.2017.0788

76. Bos FM, Snippe E, Vos SD, Hartmann JA, Wichers M. Can we jump from cross-sectional to dynamic interpretations of networks? Implications for the network perspective in psychiatry. Psychotherap Psychosom. (2017) 86:175–7. doi: 10.1159/000453583

77. Park S-C, Kim D. The centrality of depression and anxiety symptoms in major depressive disorder determined using a network analysis. J Affect Disord. (2020) 271:19–26. doi: 10.1016/j.jad.2020.03.078

78. Huang M, Wang J, Zhang R, Ni Z, Liu X, Liu W, et al. Symptom network topological features predict the effectiveness of herbal treatment for pediatric cough. Front Med. (2019) 14:357–67. doi: 10.1007/s11684-019-0699-3

79. Hopes LM, Williams A. Depression, self-defeating, and self-destructive behaviors as predictors of suicide ideation in males and females. Psychol Rep. (1999) 84:63–6. doi: 10.2466/pr0.1999.84.1.63

80. Sareen J, Houlahan T, Cox BJ, Asmundson GJG. Anxiety disorders associated with suicidal ideation and suicide attempts in the national comorbidity survey. J Nerv Ment Dis. (2005) 193:450–4. doi: 10.1097/01.nmd.0000168263.89652.6b

81. Price M, Legrand AC, Brier ZMF, Hébert-Dufresne L. The symptoms at the center: examining the comorbidity of posttraumatic stress disorder, generalized anxiety disorder, and depression with network analysis. J Psychiatr Res . (2019) 109:52–8. doi: 10.1016/j.jpsychires.2018.11.016

82. Cramer AOJ, Waldorp LJ, Han LJVD, Borsboom D. Comorbidity: a network perspective. Behav Brain Sci. (2010) 33:137–50. doi: 10.1017/S0140525X09991567

83. Boschloo L, van Borkulo CD, Rhemtulla M, Keyes KM, Borsboom D, Schoevers RA. The network structure of symptoms of the diagnostic and statistical manual of mental disorders. PLoS ONE. (2015) 10:e137621. doi: 10.1371/journal.pone.0137621

84. Kendler KS, Thornton LM, Prescott CA. Gender differences in the rates of exposure to stressful life events and sensitivity to their depressogenic effects. Am J Psychiatry. (2001) 158:587–93. doi: 10.1176/appi.ajp.158.4.587

85. Mclean CP, Anderson ER. Brave men and timid women? A review of the gender differences in fear and anxiety. Clin Psychol Rev. (2009) 29:496–505. doi: 10.1016/j.cpr.2009.05.003

86. Lazarov A, Suarez-Jimenez B, Levy O, Coppersmith DDL, Neria Y. Symptom structure of PTSD and co-morbid depressive symptoms–a network analysis of combat veteran patients. Psychol. Med. (2019) 50:2154–70. doi: 10.1017/S0033291719002034

87. Chang J, Yuan Y, Wang D. Mental health status and its influencing factors among college students during the epidemic of COVID-19. J South Med Univ . (2020) 40:171–76. doi: 10.12122/j.issn.1673-4254.2020.02.06

88. Garfin DR, Silver RC, Holman EA. The novel coronavirus (COVID-2019) outbreak: amplification of public health consequences by media exposure. Health Psychol . (2020) 5:355–57. doi: 10.1037/hea00000875

89. Banducci AN, Weiss NH. Caring for patients with posttraumatic stress and substance use disorders during the COVID-19 pandemic. Psychol Trauma. (2020) 12:S113–4. doi: 10.1037/tra0000824

90. Fried EI, Cramer AOJ. Moving forward: challenges and directions for psychopathological network theory and methodology. Perspect Psychol Sci. (2017) 12:999–1020. doi: 10.1177/1745691617705892

Keywords: network analysis, coronavirus disease 2019 (COVID-19), centrality, post-traumatic stress disorder (PTSD), suicide, public

Citation: Jiang W, Ren Z, Yu L, Tan Y and Shi C (2020) A Network Analysis of Post-traumatic Stress Disorder Symptoms and Correlates During the COVID-19 Pandemic. Front. Psychiatry 11:568037. doi: 10.3389/fpsyt.2020.568037

Received: 31 May 2020; Accepted: 29 September 2020; Published: 10 November 2020.

Reviewed by:

Copyright © 2020 Jiang, Ren, Yu, Tan and Shi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Zhihong Ren, ren@mail.ccnu.edu.cn

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings
• My Bibliography
• Collections
• Citation manager

Save citation to file

Email citation, add to collections.

• Create a new collection
• Add to an existing collection

Add to My Bibliography

Your saved search, create a file for external citation management software, your rss feed.

• Search in PubMed
• Search in NLM Catalog
• Add to Search

Visualizing the assumptions of network meta-analysis

Affiliations.

• 1 Institute of Health Data Analytics & Statistics, College of Public Health, National Taiwan University, Taipei, Taiwan.
• 2 Health Data Research Center, National Taiwan University, Taipei, Taiwan.
• 3 Education Center, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan.
• 4 Department of Surgery, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan.
• 5 Division of Biostatistics and Health Data Science, School of Public Health, University of Minnesota, Minneapolis, Minnesota, USA.
• PMID: 39313479
• DOI: 10.1002/jrsm.1760

Network meta-analysis (NMA) incorporates all available evidence into a general statistical framework for comparing multiple treatments. Standard NMAs make three major assumptions, namely homogeneity, similarity, and consistency, and violating these assumptions threatens an NMA's validity. In this article, we suggest a graphical approach to assessing these assumptions and distinguishing between qualitative and quantitative versions of these assumptions. In our plot, the absolute effect of each treatment arm is plotted against the level of effect modifiers, and the three assumptions of NMA can then be visually evaluated. We use four hypothetical scenarios to show how violating these assumptions can lead to different consequences and difficulties in interpreting an NMA. We present an example of an NMA evaluating steroid use to treat septic shock patients to demonstrate how to use our graphical approach to assess an NMA's assumptions and how this approach can help with interpreting the results. We also show that all three assumptions of NMA can be summarized as an exchangeability assumption. Finally, we discuss how reporting of NMAs can be improved to increase transparency of the analysis and interpretability of the results.

Keywords: consistency; exchangeability; homogeneity; network meta‐analysis; similarity; transitivity.

© 2024 The Author(s). Research Synthesis Methods published by John Wiley & Sons Ltd.

PubMed Disclaimer

• Lumley T. Network meta‐analysis for indirect treatment comparisons. Stat Med. 2002;21(16):2313‐2324. doi:10.1002/sim.1201
• Ades AE, Welton NJ, Dias S, Phillippo DM, Caldwell DM. Twenty years of network meta‐analysis: continuing controversies and recent developments. Res synth. Methods. 2024;15(5): 702‐727. doi:10.1002/jrsm.1700
• Song F, Altman DG, Glenny AM, Deeks JJ. Validity of indirect comparison for estimating efficacy of competing interventions: empirical evidence from published meta‐analyses. BMJ. 2003;326(7387):472. doi:10.1136/bmj.326.7387.472
• Salanti G. Indirect and mixed‐treatment comparison, network, or multiple‐treatments meta‐analysis: many names, many benefits, many concerns for the next generation evidence synthesis tool. Res Synth Methods. 2012;3(2):80‐97. doi:10.1002/jrsm.1037
• Dias S, Sutton AJ, Ades AE, Welton NJ. Evidence synthesis for decision making 2: a generalized linear modeling framework for pairwise and network meta‐analysis of randomized controlled trials. Med Decis Making. 2013;33(5):607‐617. doi:10.1177/0272989X12458724

LinkOut - more resources

Full text sources.

• Citation Manager

NCBI Literature Resources

MeSH PMC Bookshelf Disclaimer

The PubMed wordmark and PubMed logo are registered trademarks of the U.S. Department of Health and Human Services (HHS). Unauthorized use of these marks is strictly prohibited.

Information

• Author Services

Initiatives

You are accessing a machine-readable page. In order to be human-readable, please install an RSS reader.

All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited. For more information, please refer to https://www.mdpi.com/openaccess .

Feature papers represent the most advanced research with significant potential for high impact in the field. A Feature Paper should be a substantial original Article that involves several techniques or approaches, provides an outlook for future research directions and describes possible research applications.

Feature papers are submitted upon individual invitation or recommendation by the scientific editors and must receive positive feedback from the reviewers.

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

Original Submission Date Received: .

• Active Journals
• Find a Journal
• Journal Proposal
• Proceedings Series
• For Authors
• For Reviewers
• For Editors
• For Librarians
• For Publishers
• For Societies
• For Conference Organizers
• Open Access Policy
• Institutional Open Access Program
• Special Issues Guidelines
• Editorial Process
• Research and Publication Ethics
• Article Processing Charges
• Testimonials
• Preprints.org
• SciProfiles
• Encyclopedia

Article Menu

• Subscribe SciFeed
• Recommended Articles
• Author Biographies
• Google Scholar
• on Google Scholar
• Table of Contents

Find support for a specific problem in the support section of our website.

Please let us know what you think of our products and services.

Visit our dedicated information section to learn more about MDPI.

JSmol Viewer

A network reliability analysis method for complex real-time systems: case studies in railway and maritime systems.

1. Introduction

2. network reliability analysis method, 2.1. degree and degree distribution, 2.2. average path length and network diameter, 2.3. betweenness, 2.4. network topology efficiency, 2.5. reliability evaluation indices, 3. case study in railway systems, 3.1. train control system, 3.2. complex network model, 3.3. case studies, 3.3.1. node failure condition, 3.3.2. edge failure condition, 3.3.3. sensitivity analysis on failure probability assumptions.

3.3.4. Two Operating Trains

3.3.5. multiple trains operating in the same rbc jurisdiction, 3.3.6. multiple trains operating in different rbc jurisdictions, 4. case study in maritime systems, 4.1. vhf data exchange system, 4.2. complex network model, 4.3. case studies, 4.3.1. reliability analysis under node failure, 4.3.2. reliability analysis under edge failure, 4.3.3. sensitivity analysis on failure probability assumptions.

4.3.4. Operation of Multiple Nodes in a Shared Space

5. Conclusions and Future Research

Author contributions, data availability statement, conflicts of interest, abbreviations.

• Ladyman, J.; Lambert, J.; Wiesner, K. What is a complex system? Eur. J. Philos. Sci. 2013 , 3 , 33–67. [ Google Scholar ] [ CrossRef ]
• Tsiotas, D.; Polyzos, S. Analyzing the Maritime Transportation System in Greece: A Complex Network Approach. Netw. Spat. Econ. 2015 , 15 , 981–1010. [ Google Scholar ] [ CrossRef ]
• Sun, Y.; Tang, X. Cascading failure analysis of power flow on wind power based on complex network theory. J. Mod. Power Syst. Clean Energy 2014 , 2 , 411–421. [ Google Scholar ] [ CrossRef ]
• Zhao, G.L.; Xing, L.D. Reliability analysis of IoT systems with competitions from cascading probabilistic function dependence. Reliab. Eng. Syst. Saf. 2020 , 198 , 106812–106827. [ Google Scholar ] [ CrossRef ]
• Alkaff, A. Discrete time dynamic reliability modeling for systems with multistate components. Reliab. Eng. Syst. Saf. 2021 , 209 , 107462. [ Google Scholar ] [ CrossRef ]
• Wu, Y.; Sun, W. Research on the reliability allocation calculation method of a wind turbine generator set based on a vine copula correlation model. Energy Sci. Eng. 2021 , 9 , 1543–1553. [ Google Scholar ] [ CrossRef ]
• He, J.; Gao, R.; Chen, J. A sparse data-driven stochastic damage model for seismic reliability assessment of reinforced concrete structures. Reliab. Eng. Syst. Saf. 2022 , 223 , 108510. [ Google Scholar ] [ CrossRef ]
• Golmohammadi, E.; Ardakan, M.A. Reliability optimization problem with the mixed strategy, degrading components, and a periodic inspection and maintenance policy. Reliab. Eng. Syst. Saf. 2022 , 223 , 108500. [ Google Scholar ] [ CrossRef ]
• Hwang, C.L.; Tillman, F.A.; Lee, M.H. System-Reliability Evaluation Techniques for Complex/Large Systems—A Review. IEEE Trans. Reliab. 1981 , R-30 , 416–423. [ Google Scholar ] [ CrossRef ]
• Bistouni, F.; Jahanshahi, M. Analyzing the reliability of shuffle-exchange networks using reliability block diagrams. Reliab. Eng. Syst. Saf. 2014 , 132 , 97–106. [ Google Scholar ] [ CrossRef ]
• Hardy, G.; Lucet, C.; Limnios, N. K-Terminal Network Reliability Measures with Binary Decision Diagrams. IEEE Trans. Reliab. 2007 , 56 , 506–515. [ Google Scholar ] [ CrossRef ]
• Bobbio, A.; Portinale, L.; Minichino, M.; Ciancamerla, E. Improving the analysis of dependable systems by mapping fault trees into Bayesian networks. Reliab. Eng. Syst. Saf. 2001 , 71 , 249–260. [ Google Scholar ] [ CrossRef ]
• Berthomieu, B.; Diaz, M. Modeling and verification of time dependent systems using time Petri nets. IEEE Trans. Softw. Eng. 1991 , 17 , 259–273. [ Google Scholar ] [ CrossRef ]
• Cheng, Y.; Elsayed, A.E. Reliability modeling of mixtures of one-shot units under thermal cyclic stresses. Reliab. Eng. Syst. Saf. 2017 , 167 , 58–66. [ Google Scholar ] [ CrossRef ]
• Fiondella, L.; Xing, L.D. Discrete and continuous reliability models for systems with identically distributed correlated components. Reliab. Eng. Syst. Saf. 2015 , 133 , 1–10. [ Google Scholar ] [ CrossRef ]
• Park, Y.W. MILP Models for Complex System Reliability Redundancy Allocation with Mixed Components. INFORMS J. Comput. 2020 , 32 , 600–619. [ Google Scholar ] [ CrossRef ]
• Peng, W.W.; Li, Y.F.; Mi, J.H.; Yu, L.; Huang, H.Z. Reliability of complex systems under dynamic conditions: A Bayesian multivariate degradation perspective. Reliab. Eng. Syst. Saf. 2016 , 153 , 75–87. [ Google Scholar ] [ CrossRef ]
• Mi, J.H.; Li, F.Y.; Yang, Y.J.; Peng, W.W.; Huang, H.Z. Reliability assessment of complex electromechanical systems under epistemic uncertainty. Reliab. Eng. Syst. Saf. 2016 , 152 , 1–15. [ Google Scholar ] [ CrossRef ]
• Mutingi, M.; Kommula, V.P. Multi-criteria reliability optimization for a complex system with a bridge structure in a fuzzy environment: A fuzzy multi-criteria genetic algorithm approach. Eksploat. I Niezawodn.—Maint. Reliab. 2016 , 437 , 651–663. [ Google Scholar ] [ CrossRef ]
• Beyza, J.; Paricio, E.; Yusta, J. Applying Complex Network Theory to the Vulnerability Assessment of Interdependent Energy Infrastructures. Energies 2019 , 12 , 421. [ Google Scholar ] [ CrossRef ]
• Liu, H.; Hu, X.-B.; Yang, S.; Zhang, K.; Di Paolo, E. Application of Complex Network Theory and Genetic Algorithm in Airline Route Networks. Transp. Res. Rec. 2011 , 2214 , 50–58. [ Google Scholar ] [ CrossRef ]
• Dai, H.; Yan, E.; Li, N.; Bao, K.; Zhang, B. Freeway Network Connective Reliability Analysis Based on Complex Network Approach. Procedia Eng. 2016 , 137 , 372–381. [ Google Scholar ] [ CrossRef ]
• Lin, S.; Jia, L.; Wang, Y.; Qin, Y.; Li, M. Reliability Study of Bogie System of High-Speed Train Based on Complex Networks Theory. In Proceedings of the 2015 International Conference on Electrical and Information Technologies for Rail Transportation ; Springer: Berlin, Heidelberg, 2016; pp. 117–124. [ Google Scholar ]
• Feng, Y.; Qin, Y.; Kang, L.-L.; Liu, D.; Yang, X.-J.; Ma, H.-N.; Ji, L.-M. Reliability Analysis of Bogie System Based on Complex Network and Failure Propagation. In Proceedings of the International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering (QR2MSE), Zhangjiajie, China, 6–9 August 2019; pp. 1–4. [ Google Scholar ]
• Newman, M.E.J. The Structure and Function of Complex Networks. SIAM Rev. 2003 , 45 , 167–256. [ Google Scholar ] [ CrossRef ]
• Yin, X.; Mo, Y.; Dong, C.; Zhang, Y. Identification of the influential parts in a complex mechanical product from a reliability perspective using complex network theory. Qual. Reliab. Eng. Int. 2020 , 36 , 604–622. [ Google Scholar ] [ CrossRef ]
• Bian, T.; Deng, Y. Identifying Influential Nodes in Complex Networks: A Node Information Dimension Approach. Chaos Interdiscip. J. Nonlinear Sci. 2018 , 28 , 043109. [ Google Scholar ] [ CrossRef ]
• Albert, R.; Barabási, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 2002 , 74 , 47–97. [ Google Scholar ] [ CrossRef ]
• Boccaletti, S.; Latora, V.; Moreno, Y.; Chavez, M.; Hwang, D.-U. Complex networks: Structure and dynamics. Phys. Rep. 2006 , 424 , 175–308. [ Google Scholar ] [ CrossRef ]
• Xu, S.; Zhou, H.; Li, C.; Yang, X. Vulnerability Assessment of Power Grid Based on Complex Network Theory. In Proceedings of the Asia-Pacific Power and Energy Engineering Conference, Wuhan, China, 27–31 March 2009; pp. 1–4. [ Google Scholar ]
• Ali, M.A.; Jafarian, M. Power Grids as Complex Networks: Resilience and Reliability Analysis. IEEE Access 2021 , 9 , 119010–119031. [ Google Scholar ]
• Yong, Q. Statistical analysis of weighted complex network in Chinese high-speed railway. J. Railw. Sci. Eng. 2016 , 13 , 201–209. [ Google Scholar ]
• Zhang, J.; Qiang, Y.; Li, X.; Zhang, C.; Xu, D.; Wang, X. Reliability Analysis of Tianjin Urban Rail Transit Network Based on Complex Network Evolution Characteristics. Mod. Phys. Lett. B 2021 , 35 , 2150075. [ Google Scholar ] [ CrossRef ]
• Wang, Y.; Zhang, L.; Sun, S. Evaluating Network Reliability Using Topology-Based and Simulation-Based Approaches. Int. J. Crit. Infrastructures 2017 , 13 , 187–207. [ Google Scholar ]
• Chen, B.; Cai, B.; Shangguan, W.; Wang, J. Data-Driven Failure Characteristics and Reliability Analysis for Train Control On-Board Subsystem. IEEE Access 2019 , 7 , 126489–126499. [ Google Scholar ] [ CrossRef ]
• Grujicic, J. A Feasibility Study for a Satellite VHF Data Exchange System (VDES). Ph.D. Thesis, KTH Royal Institute of Technology, Stockholm, Sweden, 2019. [ Google Scholar ]
• Lázaro, F.; Raulefs, R.; Wang, W.; Clazzer, F.; Plass, S. VHF Data Exchange System (VDES): An enabling technology for maritime communications. CEAS Space J. 2018 , 11 , 55–63. [ Google Scholar ] [ CrossRef ]
• ITU-R M.2092-1 ; Technical Characteristics for a VHF Data Exchange System in the VHF Maritime Mobile Band. International Telecommunication Union: Geneva, Switzerland, 2020.
• Zhu, D.; Wang, D.; Hassan, S.-U.; Haddawy, P. Small-World Phenomenon of Keywords Network Based on Complex Network. Scientometrics 2013 , 97 , 435–442. [ Google Scholar ] [ CrossRef ]
• Bernstein, E.S.; Shore, J.C.; Jang, A.J. Network Centralization and Collective Adaptability to a Shifting Environment. Organ. Sci. 2022 , 34 , 1997–2525. [ Google Scholar ] [ CrossRef ]

Click here to enlarge figure

Share and Cite

Zang, Y.; E, J.; Fiondella, L. A Network Reliability Analysis Method for Complex Real-Time Systems: Case Studies in Railway and Maritime Systems. Mathematics 2024 , 12 , 3014. https://doi.org/10.3390/math12193014

Zang Y, E J, Fiondella L. A Network Reliability Analysis Method for Complex Real-Time Systems: Case Studies in Railway and Maritime Systems. Mathematics . 2024; 12(19):3014. https://doi.org/10.3390/math12193014

Zang, Yu, Jiaxiang E, and Lance Fiondella. 2024. "A Network Reliability Analysis Method for Complex Real-Time Systems: Case Studies in Railway and Maritime Systems" Mathematics 12, no. 19: 3014. https://doi.org/10.3390/math12193014

Article Metrics

Further information, mdpi initiatives, follow mdpi.

Subscribe to receive issue release notifications and newsletters from MDPI journals

ArcGIS API for Python

• What's New in 2.4.0
• Key features
• Get started
• Install and set up
• Release notes
• Authentication
• Visualization

Introduction

• Spatial analysis
• Data enrichment
• Deep Learning
• Geoprocessing tools
• Data engineering
• Spatially enabled dataframe
• Administration
• Content management
• System requirements
• Python environments

Guide to Network Analysis (Part 1 - Network Dataset and Network Analysis)

Network Analysis , in ArcGIS API for Python, is designed to help users answer questions like the following [1] :

• What is the quickest way to get from Manhattan to Brooklyn?
• If a fire incident is reported in downtown San Fransisco, what are the closest fire stations that can respond to the incident within five minutes' drive time?
• What are the market areas covered by the warehouses in various cities?
• What is the nearest coffee shop from my current location?
• How can we route our fleet of delivery vehicles to minimize overall transportation costs and improve customer service?
• Where should we open a new branch of our business to maximize market share?
• Our company needs to downsize—which stores should we close to maintain the most overall demand?
• What are live or historical traffic conditions like, and how do they affect my network analysis results?

These questions, asked by businesses, public services, or organizations, are related to running their operations more efficiently, and improving their strategic decision making. For instance, organizations can better understand dynamic markets, both current and potential, once they know who can access their goods or services. Transportation costs can be reduced by optimally sequencing stops and finding the shortest paths between the stops while considering several constraints such as time windows, vehicle capacities, and maximum travel times. Customer service can be improved through quicker response times or more convenient facility locations.

Figure below summarizes the most commonly used applications in network analysis.

This guide is to walk you through the commonly used Network Analysis tools, and how the above mentioned concerns or questions can be solved by ArcGIS API for Python, in the following order:

• Network Dataset and Network Analysis (You are here!)
• Find Routes ( Part 2 )
• Generate Service Area ( Part 3 )
• Find Closest Facility ( Part 4 )
• Generate Origin Destination Cost Matrix ( Part 5 )
• Solve Location Allocation ( Part 6 )
• Vehicle Routing Problem Service ( Part 7 )

Please refer to the road map above if you want to jump to the next topic. Otherwise, if you choose to stay with us, in part 1, you will get to know network dataset , and other preconditions needed to solve a network analysis problem.

In the rest of the guide, Part 2 introduces finding the quickest, shortest, or even the most scenic route, depending on the impedance you choose to solve for; Part 3 guides you in finding service areas (a.k.a. a region that encompasses all accessible streets (that is, streets that are within a specified impedance) around any location on a network; Part 4 walks you through steps in measuring the cost of traveling between incidents and facilities and determining which are nearest to one another; Part 5 talks about how to find and measure the least-cost paths along the network from multiple origins to multiple destinations; Part 6 demonstrates processes in deciding the optimized allocation of new locations for facilities. More advanced topics such as Vehicle Routing problem, of which the goal is to best service the orders and minimize the overall operating cost for the fleet of vehicles will be covered in Part 7 .

If you are new to Network Analysis or in need of a refresher of the concepts, the Youtube video below would serve as a good introduction to the key ideas:

What is a network?

A network is a system of interconnected elements, such as edges (lines) and connecting junctions (points), that represent possible routes from one location to another [1] ..

People, resources, and goods tend to travel along networks: cars and trucks travel on roads, airliners fly on predetermined flight paths, and oil flows in pipelines. By modeling potential travel paths with a network, it is possible to perform analyses related to the movement of the oil, trucks, or other agents on the network. The most common network analysis is finding the shortest path between two points.

ArcGIS groups networks into two categories: utility networks and network datasets. This guide will only cover the second category, in order to learn more about utility network, please refer to here .

Network Dataset

In order to model transportation networks, Network Datasets are created from source features, which can include simple features (lines and points) and turns, and store the connectivity of the source features. When you perform a network analysis, it is always done on a network dataset [3] .

Also, Network Datasets contain Network elements. Network elements are generated from the source features used to create the network datasets. The geometry of the source features helps establish connectivity. In addition, network elements have attributes that control navigation over the network [4] .

The following are the three types of network elements:

• Edges —Edges connect to other elements (junctions) and are the links over which agents travel. Line feature classes participate as edge feature sources.
• Junctions —Junctions connect edges and facilitate navigation from one edge to another. Point feature classes can participate as junction feature sources, but multipoint feature classes cannot.
• Turns —Turns store information that can affect movement between two or more edges. Turn feature classes participate as turn feature sources in a network. A turn feature source models a subset of possible transitions between edge elements during navigation.

Edges and junctions form the basic structure of a network. Connectivity in a network deals with connecting edges and junctions to each other. Turns are optional elements that store information about a particular turning movement; for instance, a left turn is restricted from one particular edge to another.

Multimodal Network Dataset

Multimodal Network Datasets are used for transportation situations when the set of [origin, destination] remain the same, but performed with two or more different modes of transport. For example, constructing a transportation network in downtown Paris in roads, railways, and buses would lead to multimodal network datasets [3] .

3D Network Dataset

Three-dimensional network datasets enable you to model the interior pathways of buildings, mines, caves, and so on. If you have street features with accurate z-coordinate values, you can use them with z-aware features that model pathways inside buildings to create 3D networks of campuses or even cities. This allows you to answer questions such as (1) What is the best wheelchair-accessible route between rooms in different buildings? (2) What floors of a high-rise building can't be reached by a fire department within eight minutes? [1]

Network Analysis Services

Network Analysis (NA) services are being called by the ArcGIS Network Analysis solvers (e.g. route, closest facility, service area, location-allocation, origin-destination cost matrix, and the vehicle routing problem). Users can choose between ready-to-use NA services hosted on ArcGIS Online, or customized NA services on enterprise that they have previously published and configured by themselves. If you perform an analysis using ArcGIS Online, the solver references a high-quality, worldwide network datasets stored in the ArcGIS Online cloud and will use ArcGIS Online credits. If you're using your own data, no online credits are used, but you need to associate your network datasets with the project [1] .

With ArcGIS Online network analysis services, you can also view historical, live, and predicted traffic conditions without creating or purchasing a network dataset or an ArcGIS Network Analyst extension license. The services reference high-quality street data that is updated periodically.

To access these services, you need an ArcGIS organizational account with the network analysis privilege, and the application must be connected to ArcGIS Online. If you are licensing ArcGIS Pro through an ArcGIS Online account, you are probably signed in to the application already. These services consume credits when they are run. Please refer to developers website or ArcGIS help doc for more information with credits.

Ready-to-use NA services on ArcGIS Online have provided convenience to users. However, there are situations where users prefer to use the customized NA services instead. For example, when the ArcGIS Online organization that users belong to has run of credits, or users need to keep the entire NA solving process in private and not allowed to share with others, or from a perspective of computational resources' concerns that the CPU or memory resources to be consumed by the solver would have exceeded the limitations of ArcGIS Online, then users need to consider the alternative approach, to use the customized NA services on Enterprise.

What's next?

Multiple solver methods are available for fulfilling the requirements for routing, generating service areas, finding closest facilities, etc., and for the same operation, user can choose between two API methods - as defined in the arcgis.network.analysis and arcgis.features.use_proximity modules respectively. These implementations will be covered in the following Part 2 , Part 3 , and Part 4 .

For instance, for the routing operation, you can choose from network.analysis.find_routes and features.use_proximity.plan_routes , as demonstrated in the table above. The differences between APIs in these two modules are:

• network.analysis methods are comparatively faster, and can help solve bigger problems which require more time and resources from the server;
• network.analysis tools can be considered as coarse-grained online widgets that aim to solve problems in a simpler way;
• network.analysis contains all capabilities required for network analysis processes while features.use_proximity only contains a subset ;
• features.use_proximity is workflow-driven, and Web GIS Oriented (a.k.a. with which user can input a Feature Service, and get the output as Feature Service), while the network.analysis tools take input parameters and return output variable as in-memory FeatureCollection .
• In situations where the output Feature Collection is oversized, ArcGIS API for Python suggests users to implement a features.use_proximity workflow so that output can be handled on the server side and be saved as a Feature Service (since processing and creating FeatureSet as output can take much more memory and computation time).

Conclusions

Part 1 has introduced network dataset, network analysis, and modules provided in ArcGIS API for Python needed to solve a network analysis problem. Next, let's move onto Part 2 which demonstrates how to find the quickest, shortest, or even the most scenic route, depending on the impedance you choose to solve for.

[1] "What is network analyst", https://pro.arcgis.com/en/pro-app/help/analysis/networks/what-is-network-analyst-.htm , accessed on September 2019

[2] Deelesh Mandloi, "Network Analysis Services in ArcGIS Enterprise", http://proceedings.esri.com/library/userconf/proc17/tech-workshops/tw_419-218.pdf , last accessed on 09/09/2019

[3] "What is a network dataset", https://pro.arcgis.com/en/pro-app/help/analysis/networks/what-is-network-dataset-.htm , accessed on September 2019

[4] "Network elements", https://pro.arcgis.com/en/pro-app/help/analysis/networks/network-elements.htm , accessed on September 2019

[5] "New Network Analysis Layer", https://pro.arcgis.com/en/pro-app/help/analysis/networks/new-network-analysis-layer.htm , accessed on 09/09/2019

Your browser is no longer supported. Please upgrade your browser for the best experience. See our browser deprecation post for more details .

• - Google Chrome

Intended for healthcare professionals

• My email alerts
• BMA member login
• Username * Password * Forgot your log in details? Need to activate BMA Member Log In Log in via OpenAthens Log in via your institution

Search form

• Advanced search
• Search responses
• Search blogs
• Comparative effects of...

Comparative effects of drug interventions for the acute management of migraine episodes in adults: systematic review and network meta-analysis

• Related content
• Peer review
• William K Karlsson , doctoral student 1 2 ,
• Edoardo G Ostinelli , consultant psychiatrist and senior researcher 3 4 5 ,
• Zixuan A Zhuang , doctoral student 1 2 ,
• Lili Kokoti , postdoctoral clinical scientist 1 2 ,
• Rune H Christensen , doctoral student 1 2 ,
• Haidar M Al-Khazali , doctoral student 1 2 ,
• Christina I Deligianni , consultant neurologist 6 7 ,
• Anneka Tomlinson , postdoctoral academic clinical fellow 3 4 5 ,
• Håkan Ashina , postdoctoral research fellow 1 2 ,
• Elena Ruiz de la Torre , executive director 8 ,
• Hans-Christoph Diener , professor of neurology emeritus 9 ,
• Messoud Ashina , professor of neurology and director of the Human Migraine Research Unit at the Danish Headache Centre 1 2 10
• 1 Department of Neurology, Danish Headache Centre, Copenhagen University Hospital – Rigshospitalet, Copenhagen, Denmark
• 2 Department of Clinical Medicine, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
• 3 Department of Psychiatry, University of Oxford, Oxford, UK
• 4 Oxford Precision Psychiatry Lab, National Institute for Health Research (NIHR) Oxford Health Biomedical Research Centre, University of Oxford, Oxford, UK
• 5 Warneford Hospital, Oxford Health NHS Foundation Trust, Oxford, UK
• 6 Department of Neurology, Athens Naval Hospital, Athens, Greece
• 7 1st Department of Neurology, Aeginition Hospital, National and Kapodistrian University of Athens, Athens, Greece
• 8 European Migraine and Headache Alliance, Brussels, Belgium
• 9 Department of Neuroepidemiology, Institute for Medical Informatics, Biometry and Epidemiology, University Duisburg-Essen, Essen, Germany
• 10 Danish Knowledge Centre on Headache Disorders, Copenhagen University Hospital – Rigshospitalet, Copenhagen, Denmark
• Correspondence to: A Cipriani andrea.cipriani{at}psych.ox.ac.uk (or @And_Cipriani )
• Accepted 10 July 2024

Objective To compare all licensed drug interventions as oral monotherapy for the acute treatment of migraine episodes in adults.

Design Systematic review and network meta-analysis.

Data sources Cochrane Central Register of Controlled Trials, Medline, Embase, ClinicalTrials.gov, EU Clinical Trials Register, WHO International Clinical Trials Registry Platform, as well as websites of regulatory agencies and pharmaceutical companies without language restrictions until 24 June 2023.

Methods Screening, data extraction, coding, and risk of bias assessment were performed independently and in duplicate. Random effects network meta-analyses were conducted for the primary analyses. The primary outcomes were the proportion of participants who were pain-free at two hours post-dose and the proportion of participants with sustained pain freedom from two to 24 hours post-dose, both without the use of rescue drugs. Certainty of the evidence was graded using the confidence in network meta-analysis (CINeMA) online tool. Vitruvian plots were used to summarise findings. An international panel of clinicians and people with lived experience of migraine co-designed the study and interpreted the findings.

Eligibility criteria for selecting studies Double blind randomised trials of adults (≥18 years) with a diagnosis of migraine according to the International Classification of Headache Disorders.

Results 137 randomised controlled trials comprising 89 445 participants allocated to one of 17 active interventions or placebo were included. All active interventions showed superior efficacy compared with placebo for pain freedom at two hours (odds ratios from 1.73 (95% confidence interval (CI) 1.27 to 2.34) for naratriptan to 5.19 (4.25 to 6.33) for eletriptan), and most of them also for sustained pain freedom to 24 hours (odds ratios from 1.71 (1.07 to 2.74) for celecoxib to 7.58 (2.58 to 22.27) for ibuprofen). In head-to-head comparisons between active interventions, eletriptan was the most effective drug for pain freedom at two hours (odds ratios from 1.46 (1.18 to 1.81) to 3.01 (2.13 to 4.25)), followed by rizatriptan (1.59 (1.18 to 2.17) to 2.44 (1.75 to 3.45)), sumatriptan (1.35 (1.03 to 1.75) to 2.04 (1.49 to 2.86)), and zolmitriptan (1.47 (1.04 to 2.08) to 1.96 (1.39 to 2.86)). For sustained pain freedom, the most efficacious interventions were eletriptan and ibuprofen (odds ratios from 1.41 (1.02 to 1.93) to 4.82 (1.31 to 17.67)). Confidence in accordance with CINeMA ranged from high to very low. Sensitivity analyses on Food and Drug Administration licensed doses only, high versus low doses, risk of bias, and moderate to severe headache at baseline confirmed the main findings for both primary and secondary outcomes.

Conclusions Overall, eletriptan, rizatriptan, sumatriptan, and zolmitriptan had the best profiles and they were more efficacious than the recently marketed drugs lasmiditan, rimegepant, and ubrogepant. Although cost effectiveness analyses are warranted and careful consideration should be given to patients with a high risk cardiovascular profile, the most effective triptans should be considered as preferred acute treatment for migraine and included in the WHO List of Essential Medicines to promote global accessibility and uniform standards of care.

Systematic review registration Open Science Framework https://osf.io/kq3ys/ .

• Download figure
• Open in new tab
• Download powerpoint

Introduction

Migraine is a neurological disorder characterised by disabling, recurrent episodes of moderate to severe headache and accompanying symptoms lasting up to 72 hours. 1 Migraine affects more than one billion people worldwide and is the leading cause of disability in girls and women aged 15 to 49 years. 2 The burden of migraine extends to personal welfare, reduced productivity, and poor socioeconomic outcomes. 3

The acute management of migraine episodes consists of drug interventions aimed at providing rapid and sustained pain relief, and, ideally, freedom from pain. 4 Several drugs with different mechanisms of action are available. 1 International clinical guidelines generally endorse non-steroidal anti-inflammatory drugs (NSAIDs) as initial treatment, whereas triptans are recommended for moderate to severe episodes or when the response to NSAIDs is insufficient. 5 6 7 8 In recent years, lasmiditan and gepants have been introduced as further treatment options, 1 especially for patients with contraindications to triptans owing to potential vasoconstrictive effects and higher risk of ischaemic events. 9 10 However, no clear consensus exists as to which specific agents from these drug classes should be selected initially.

Given the wide range of drugs for acute treatment of migraine, clinicians and patients need robust evidence to make the best, individualised choice in routine practice. Network meta-analyses allow for estimation of comparative efficacy, providing a comprehensive summary of the evidence base and understanding of the relative merits of the multiple interventions. 11 Previous network meta-analyses, however, only compared a subset of available drugs. 12 13 14 15 16 17 18 19 20 21 As part of the AMADEUS (acute migraine attacks: different effects of individual drugs) “project,” we conducted a systematic review and network meta-analysis to compare licensed oral drugs for the acute treatment of migraine episodes in adults.

Information sources and eligibility criteria

Full details about the methods are reported in the protocol (see supplementary appendix 1), which has been registered in Open Science Framework ( https://osf.io/kq3ys/ ). Our reporting of the study adhered to the guidelines outlined in the PRISMA (preferred reporting items for systematic reviews and meta-analyses) statement for systematic reviews incorporating network meta-analyses. 22

We searched for published and unpublished studies in the Cochrane Central Register of Controlled Trials, Medline, Embase, ClinicalTrials.gov, EU Clinical Trials Register, WHO (World Health Organization) International Clinical Trials Registry Platform, as well as websites of regulatory agencies and pharmaceutical companies without language restrictions until 24 June 2023 (see supplementary appendix 2 for full search strategy).

We included double blind, randomised controlled trials comparing monotherapy using oral drugs with placebo or another eligible active treatment for the acute treatment of migraine episodes in adults (≥18 years). Participants were outpatients with a diagnosis of migraine according to the International Classification of Headache Disorders. 23 24 25 26 Only drugs and treatment dose ranges licensed for migraine or headache were considered eligible if they were recommended by at least one of the regulatory bodies internationally (also see supplementary appendix 3 and table S1): the British National Formulary (UK), the Federal Institute for Drugs and Medical Devices (Germany), the European Medicines Agency, the National Agency for the Safety of Medicines and Health Products (France), the Pharmaceuticals and Medical Devices Agency (Japan), the Therapeutic Goods Administration (Australia), and the US Food and Drug Administration (FDA). We did not include opiates as clinical guidelines discourage their use for migraine owing to limited efficacy, considerable adverse effects, and risk of dependency. 4 6 We excluded studies set in emergency departments as people attending these due to migraine usually represent a subgroup with particularly severe or atypical episodes. 27

Pairs of researchers independently screened and selected the studies, reviewed published and unpublished reports, extracted data from the included trials, and assessed risk of bias. 28 Any discrepancies were resolved by discussion with the other members of the team.

We selected outcomes recommended by the International Headache Society. 29 The primary outcomes were the proportion of participants who were pain-free at two hours post-dose and the proportion of participants with sustained pain freedom from two to 24 hours post-dose, both without the use of rescue drugs.

Secondary outcomes included the proportion of participants with pain relief at two hours post-dose, the proportion with pain relapse within two to 48 hours post-dose, and the proportion using rescue drugs after two hours and up to 24 hours. We also investigated safety and tolerability, assessing the proportion of participants who experienced at least one serious adverse event and the proportion with at least one of 19 specific clinically relevant adverse events predefined in the protocol (see supplementary appendix 1).

Summary measures and synthesis

The intention-to-treat principle was applied by using the number of patients randomised as the denominator in all analyses and assuming that patients with missing information had a negative outcome. We evaluated the assumption of transitivity (ie, that valid indirect comparisons could be made through the network because the distribution of effect modifiers on average was similar between the compared sets of trials) 30 by comparing the distribution of the several potential effect modifiers across comparisons for our primary outcomes: mean age, 31 sex (ie, the proportion of female participants), 32 headache intensity at baseline (ie, the proportion of participants with moderate or severe pain), 33 and ongoing use of preventive migraine drugs. 34 Global and local approaches were used to assess the inconsistency between direct and indirect sources of evidence. 35 To assess the inconsistency globally, we used a design-by-treatment test, 36 whereas for local inconsistency we used back calculation and separated indirect from direct design evidence methods to compare direct and indirect evidence for each pairwise treatment comparison. 37 Statistical heterogeneity was assessed for each pairwise and network meta-analysis comparison using τ 2 and I 2 statistics. 11

We conducted a series of network meta-analyses using a random effects model within a frequentist setting, assuming equal heterogeneity across all comparisons and accounting for correlations induced by multi-arm studies. For studies with rare events (ie, an event rate of <5%), we used a common effect Maentel-Haenszel approach. 37 We conducted the network meta-analyses using the “netmeta” package in R (version 4.2.2). We estimated effect sizes from pairwise and network meta-analyses by summary odds ratios for dichotomous outcomes with corresponding 95% confidence intervals (CIs).

League tables and vitruvian plots were used to present the findings from the network meta-analyses. 37 The vitruvian plot is a benefit-harm communication tool to summarise direction, magnitude, and uncertainty of effects over multiple outcomes in network meta-analysis. 38 For the vitruvian plots, we selected sumatriptan as the reference intervention as it is the most commonly prescribed migraine specific drug and it is included in the WHO Model List of Essential Medicines. 39 As secondary analyses, we also visualised results using forest plots and vitruvian plots with placebo or ibuprofen as reference treatments.

The risk of bias of individual studies was assessed on each primary outcome with the Cochrane risk of bias tool, version 2.0 (RoB2), 28 and the certainty of evidence was assessed using the confidence in network meta-analysis (CINeMA) framework. 40

Additional analyses

We evaluated possible heterogeneity of treatment effects using bayesian network meta-regressions for sex assigned at birth and presence of aura. To evaluate the robustness of our findings, we carried out the following sensitivity analyses on our primary outcomes: trials only with doses licensed by the FDA, with low risk of bias, with participants experiencing moderate or severe headache, with a diagnosis of menstrual related migraine, splitting nodes with high and low doses, assessed the effect of placebo response, excluding studies with participants with medical comorbidity, or excluding studies that allowed the use of preventive drugs.

Patient and public involvement

We discussed the aims and design of this study with members of the public, including those who had experienced migraine (one patient representative is a coauthor of this paper and has been involved in all stages of the project). We used their feedback to guide the selection of outcomes for the study and inform the interpretation of the results presented in this manuscript. Three members of the research team conducted statistical analyses and presented the results in a blinded fashion (ie, the names of the interventions were masked to reduce bias from previous experience or knowledge) to two independent panels of expert clinicians and patient representatives from international organisations in Argentina, Canada, Europe, and the US.

Study selection and network geometry

Overall, 184 double blind randomised controlled trials published between 1991 and 2023 were identified ( fig 1 ). Supplementary appendix 4 and tables S3 and S4 describe the included studies. Of those studies, 174 (95%) were sponsored by the pharmaceutical industry, 163 (89%) were placebo controlled, and 52 (28%) directly compared at least two eligible active interventions. Seventy six trials were from North America (41%), 47 from Europe (26%), 16 from Asia (9%), and 37 recruited participants from more than one continent (20%). We retrieved unpublished information for 124 (67%) trials. The median study sample size was 378 (interquartile range 132-690) participants, mean age 40.3 (standard deviation 10.9) years, 85.6% of the total sample were female participants, and 32.3% had a history of migraine with aura.

Study selection process. *See supplementary appendix table S2 for full list

Overall, 137 randomised controlled trials were included in the network meta-analyses, with 62 682 participants allocated to drug treatment and 26 763 to placebo. The 17 individual drugs were divided into five categories: antipyretics (paracetamol), ditans (lasmiditan), gepants (rimegepant and ubrogepant), NSAIDs (acetylsalicylic acid, celecoxib, diclofenac potassium, ibuprofen, naproxen sodium, and phenazone), and triptans (almotriptan, eletriptan, frovatriptan, naratriptan, rizatriptan, sumatriptan, and zolmitriptan). All interventions had at least one placebo controlled trial for one or more outcomes ( fig 2 and fig 3 ) and most networks were well connected (see supplementary appendix 5). The full dataset and information for the vitruvian plots are freely available online at GitHub ( https://github.com/EGOstinelli/NMA-on-migraine/ ).

Network plots of eligible direct comparisons for primary and secondary efficacy outcomes and any serious adverse events. Line width is proportional to the number of trials comparing each pair of treatments. Node size is proportional to the number of randomised participants

Network plots of eligible direct comparisons for six specific non-serious adverse events considered most important by clinician and patient representative panels. Line width is proportional to the number of trials comparing each pair of treatments. Node size is proportional to the number of randomised participants. See supplementary appendix 5 for network plots of the remaining specific adverse events

Synthesis of results and certainty of evidence

Figure 4 and figure 5 show the results of the network meta-analyses. Further results are available in supplementary appendices 6-9. All active interventions were more efficacious than placebo for pain freedom at two hours (odds ratios from 1.73 (95% CI 1.27 to 2.34) for naratriptan to 5.19 (4.25 to 6.33) for eletriptan) and most were also efficacious for sustained pain freedom from two to 24 hours post-dose, except paracetamol and naratriptan (odds ratio 1.66 (0.68 to 4.04) and 1.57 (0.76 to 3.25), respectively). When the active interventions were compared with each other, eletriptan was superior to almost all the other drugs for achieving pain freedom at two hours, followed by rizatriptan, sumatriptan, and zolmitriptan (odds ratios from 1.35 to 3.01). For sustained pain freedom up to 24 hours, the most efficacious interventions were eletriptan (odds ratios from 1.41 to 2.73) and ibuprofen (odds ratios from 3.16 to 4.82). In terms of secondary efficacy outcomes, all interventions were superior to placebo for pain relief at two hours and for use of rescue drugs from two to 24 hours.

Network meta-analysis for efficacy of drugs (in alphabetical order) for the acute treatment of migraine (freedom from pain, sustained pain freedom, pain relief, and use of rescue drugs). Comparisons should be read from left to right. Comparative estimates (reported as odds ratios with corresponding 95% confidence intervals) are located at the intersection between the treatment defined by the column and the treatment defined by the row. Bottom left rectangle: For pain freedom and sustained pain freedom from two to 24 hours, estimates >1 favour the treatment defined by the column. Top right rectangle: for pain relief, estimates >1 favour the treatment defined by the row. For use of rescue drugs, estimates <1 favour the treatment defined by the row. Emboldened numbers represent estimates where the confidence interval is either >1 or <1. Certainty of the evidence (according to confidence in network meta-analysis (CINeMA)) for the two primary outcomes is presented: *=high certainty of evidence; †=moderate certainty of evidence; ‡=low certainty of evidence; §=very low certainty of evidence. ASA=acetylsalicylic acid; ALM=almotriptan; CEL=celecoxib; DIC=diclofenac potassium; ELE=eletriptan; FRO=frovatriptan; IBU=ibuprofen; LAS=lasmiditan; NAP=naproxen sodium; NAR=naratriptan; PAR=paracetamol; PHE=phenazone; RIM=rimegepant; RIZ=rizatriptan; SUM=sumatriptan; UBR=ubrogepant; ZOL=zolmitriptan

Network meta-analysis for adverse events (dizziness, fatigue, nausea, and sedation) associated with drugs (in alphabetical order) for the acute treatment of migraine. Comparisons should be read from left to right. Comparative estimates are located at the intersection between the treatment defined by the column and the treatment defined by the row. Data are presented as odds ratio with corresponding 95% confidence intervals. Bottom left rectangle: for dizziness and nausea, estimates <1 favour the treatment defined by the column. Top right rectangle: for sedation and fatigue, estimates <1 favour the treatment defined by the row. Emboldened numbers represent estimates where the confidence interval of the comparative estimate is either >1 or <1. ASA=acetylsalicylic acid; ALM=almotriptan; CEL=celecoxib; DIC=diclofenac potassium; ELE=eletriptan; FRO=frovatriptan; IBU=ibuprofen; LAS=lasmiditan; NAP=naproxen sodium; NAR=naratriptan; PAR=paracetamol; PHE=phenazone; RIM=rimegepant; RIZ=rizatriptan; SUM=sumatriptan; UBR=ubrogepant; ZOL=zolmitriptan

When the drugs were compared head to head, eletriptan was associated with better efficacy than nearly all of the other active interventions for pain relief at two hours (odds ratios from 1.26 to 2.63) and use of rescue drugs (odds ratios from 0.43 to 0.63). Outcome data on pain relapse up to 48 hours were only available for lasmiditan, sumatriptan, and rimegepant: all showed greater efficacy than placebo, with comparable performances for lasmiditan (odds ratio 0.42 (95% CI 0.12 to 1.48)) and rimegepant (0.29 (0.08 to 1.03)) relative to sumatriptan. For adverse events, dizziness was more commonly associated with lasmiditan, eletriptan, sumatriptan, and zolmitriptan (odds ratios from 1.14 to 3.19). Fatigue and sedation occurred more frequently with eletriptan (odds ratios from 1.34 to 2.63) and lasmiditan (odds ratios from 1.33 to 2.50). Paraesthesia was more often associated with lasmiditan (odds ratios from 1.28 to 1.50), sumatriptan (odds ratio versus placebo 1.18 (95% CI 1.04 to 1.32)), and zolmitriptan (odds ratios from 1.18 to 1.50). Nausea was also more likely to be experienced with lasmiditan, sumatriptan, zolmitriptan, and ubrogepant (odds ratios from 1.19 to 2.22). Paracetamol was, conversely, less likely to be associated with nausea (odds ratios from 0.44 to 0.56) but more likely to be associated with hepatic toxicity (odds ratios from 6.40 to 7.69). Eletriptan was the only intervention more frequently associated with chest pain or discomfort (odds ratios from 1.42 to 1.78).

The vitruvian plots show the 10 outcomes deemed the most clinically relevant by the panel of expert clinicians and patient representatives (pain freedom at two hours, sustained pain freedom from two to 24 hours, pain relief at two hours, use of rescue drugs within two to 24 hours, chest pain or discomfort, dizziness, fatigue, nausea, paraesthesia, and sedation) using sumatriptan as the reference drug ( fig 6 and fig 7 ). Supplementary appendix 10 shows the vitruvian plots using placebo and ibuprofen as reference interventions.

Vitruvian plots of each active intervention (in alphabetical order) compared with sumatriptan (reference drug) across key outcomes. Efficacy is reported in the bottom wedges by four outcomes: freedom from pain at two hours, sustained pain freedom from two to 24 hours, pain relief at two hours, and use of rescue drugs from two to 24 hours. Tolerability is reported in the lateral and top wedges by the specific adverse events of chest pain or discomfort, dizziness, fatigue, nausea, paraesthesia, and sedation. Colour indicates the relative performance of the intervention of interest and the precision of the estimate in comparison with sumatriptan (reference drug), from green (the intervention is better than sumatriptan), to yellow (unclear whether the drug performs better or worse than sumatriptan), and to red (the intervention is worse than sumatriptan). The more precise the estimate is, the more intense the colours. Estimated event rates are expressed as absolute percentages. The wedge titles are coloured to indicate availability of data for the analyses (if no data are available for the analyses, the wedge titles are white (ie, without any colour)). Supplementary appendix 10 provides further details, including vitruvian plots with ibuprofen or placebo as the reference intervention

Continued: Vitruvian plots of each active intervention (in alphabetical order) compared with sumatriptan (reference drug) across key outcomes. Efficacy is reported in the bottom wedges by four outcomes: freedom from pain at two hours, sustained pain freedom from two to 24 hours, pain relief at two hours, and use of rescue drugs from two to 24 hours. Tolerability is reported in the lateral and top wedges by the specific adverse events of chest pain or discomfort, dizziness, fatigue, nausea, paraesthesia, and sedation. Colour indicates the relative performance of the intervention of interest and the precision of the estimate in comparison with sumatriptan (reference drug, blue), from green (the intervention is better than sumatriptan), to yellow (unclear whether the drug performs better or worse than sumatriptan), and to red (the intervention is worse than sumatriptan). The more precise the estimate is, the more intense the colours. Estimated event rates are expressed as absolute percentages. The wedge titles are coloured to indicate availability of data for the analyses (if no data are available for the analyses, the wedge titles are white (ie, without any colour)). Supplementary appendix 10 provides further details, including vitruvian plots with ibuprofen or placebo as the reference intervention

The certainty of the evidence for the primary outcomes assessed using CINeMA ranged from high to very low. Rimegepant versus placebo was the only comparison rated high certainty for each primary outcome. For pain freedom at two hours, 13 of 153 (8%) comparisons were rated moderate certainty, 26 (17%) were rated low certainty, and 113 (74%) were rated very low certainty. For sustained pain freedom until 24 hours, 4 of 105 (4%) comparisons were rated moderate, 5 (5%) were rated low, and 95 (90%) were rated very low. Supplementary appendix 11 and tables S5, and S6 provide full information about CINeMA. Risk of bias assessed using the Cochrane risk of bias 2 tool (RoB2) was rated low for pain freedom at two hours in 24 of 115 (21%) randomised controlled trials, some concerns in 73 (63%), and high in 18 (16%). For sustained pain freedom, risk of bias was rated low in 16 of 56 (29%) randomised controlled trials, some concerns in 34 (61%), and high in 6 (11%). See supplementary appendix 12 and tables S7 and S8 for further information on risk of bias.

Credibility assessment and sensitivity analyses

Measures of statistical heterogeneity (τ 2 and I 2 ) and inconsistency for each outcome are shown in supplementary appendix 13 as well as for subgroup and sensitivity analyses in supplementary appendices 14 and 15. No violations of our transitivity assumptions were identified. Inconsistencies were observed among comparisons for the outcomes of pain freedom at two hours (8%), sustained pain freedom (5%), use of rescue drugs (9%), dizziness (8%), chest pain or discomfort (13%), and sedation (5%). We checked the data for potential extraction or entering errors, but no mistakes were identified.

We considered changes in the magnitude of the placebo response as a potential explanation of heterogeneity and inconsistency. To explore this, we did a meta-regression of the log proportion of placebo responders over time for each primary outcome, which showed a structural break corresponding to the year 1997 for pain freedom at two hours. A sensitivity analysis restricted to studies after 1997 resulted in comparable results. Overall, sensitivity analyses on FDA licensed doses only, high versus low doses, risk of bias, and moderate-to-severe headache at baseline confirmed our main findings (see supplementary appendix 15).

Compared with previous studies, our systematic review and network meta-analysis provided comprehensive data synthesis on the acute treatment of migraine in adults. 21 41 Our findings showed that some triptans—namely, eletriptan, rizatriptan, sumatriptan, and zolmitriptan—had the most favourable overall profiles in terms of efficacy and tolerability. These four triptans were more efficacious than the most recently marketed drugs lasmiditan, rimegepant, and ubrogepant, which, based on our results, showed efficacy comparable to that of paracetamol and most NSAIDs.

Triptans are selective serotonin (5 hydroxytryptamine) 1B / 1D receptor agonists, exhibiting differences in receptor affinity, lipophilicity, metabolism, and pharmacokinetic profiles within the same class. 4 Despite their low acquisition costs and balanced efficacy and tolerability profiles, however, triptans remain underused among people with migraine. 42 43 In the US, current use of triptans ranges from 16.8% to 22.7%, 43 and in Europe from 3.4% to 22.5%. 42 Triptans are contraindicated in patients with vascular disease, posing an important limitation to their use. 4 However, concerns about their cardiovascular safety remain difficult to interpret, as cerebrovascular events may present primarily as migraine-like headaches, and misdiagnosis of transient ischaemic attack and minor stroke as migraine is not rare. 44 45 Moreover, studies assessing the response to high dose intravenous eletriptan or subcutaneous sumatriptan found no clinically significant vasoconstriction in patients undergoing diagnostic coronary angiography. 9 Future studies revisiting the vascular contraindications of triptans are crucial to minimise potentially missed treatment opportunities.

The most recently marketed drugs, such as lasmiditan, rimegepant, and ubrogepant, are not associated with vasoconstrictive effects and have therefore been promoted as alternatives for patients for whom triptans are contraindicated or not tolerated. 4 While rimegepant was well tolerated based on the results in our study, ubrogepant showed increased risk of nausea compared with placebo. Lasmiditan was associated with a substantial risk of dizziness, along with paraesthesia and sedation. Restrictions raised by the FDA against driving for eight hours after intake of lasmiditan underscore the challenges to its use. 1 Moreover, the high costs of these new drugs pose a barrier to their widespread use and necessitate trials to ascertain their cost effectiveness for patients with insufficient response to triptans. 1 Notably, our search identified one ongoing study, with pending results, in participants for whom triptans were unsuitable owing to lack of efficacy, previous intolerance, or contraindications. 46

Our results showed wide variation in performance across individual NSAIDs. Diclofenac potassium showed efficacy and tolerability close to that of sumatriptan, but these estimates were imprecise due to the large confidence intervals. For ibuprofen, the high efficacy estimate for sustained pain freedom was driven by a single study with a noticeably low placebo response. Acetylsalicylic acid and naproxen sodium showed moderate efficacy, with tolerability comparable to that of sumatriptan. Celecoxib ranked lowest among NSAIDs, whereas sparse evidence was available for phenazone. Taken together, NSAIDs performed worse than triptans, were comparable to gepants, and were less likely to cause adverse events compared with lasmiditan. Paracetamol, although showing limited effect for pain freedom at two hours, proved to be well tolerated, affirming its role as a viable option for those seeking pain relief with low risk of adverse events.

Strengths and limitations of this study, and future directions

Using the websites of regulatory agencies and international trial registries, and contacting study authors and pharmaceutical companies, we managed to incorporate a large amount of unpublished data in the analysis. Nowadays, online archives exist where trials are prospectively registered, which makes the study search more reliable; however, these registries only collect transparent information about the most recent studies, and we cannot rule out the possibility that some studies were missing or that the same studies were counted twice in our analyses. By making the dataset fully and freely available, we welcome any information that might help clarify mistakes in our meta-analysis.

Our findings have some limitations. Moderate heterogeneity was found for most outcomes and, according to our ratings in CINeMA, confidence in our findings was low or very low for most comparisons. Lower confidence levels were often due to the lack of prespecified analysis plans (within study bias), imprecision of treatment effects, or lack of information about randomisation and allocation concealment. Considering all this, the risk of bias for many studies may largely be a matter of reporting. 47 To increase the methodological rigour of the contributing evidence, we included only double blind trials, which are similar in design, patient populations, and conduct. 48 49 Available networks were in general adequately connected, with placebo or sumatriptan being the most connected interventions and thus increasing the reliance on indirect evidence. We investigated the impact of study year on our primary efficacy outcomes and found no effect on the results of our network meta-analyses. The temporal trend of the placebo response in trials of acute treatments for migraine episodes warrants further investigations owing to its relevance for planning of sample size in future trials and for network meta-analysis. Although our results enhance the choice of drugs based on personal preferences in relation to efficacy and risk of adverse events, our findings were limited to average treatment effects due to the lack of individual patient data. Since monotherapy drugs are generally preferred for treatment, we did not include combination drugs. To avoid violation of transitivity, we restricted our focus to oral treatments, although the drugs can be administered by alternative routes. 4 Finally, in the present study we did not consider type of oral formulation, consistency in response across migraine episodes, or cost effectiveness. We also did not cover important clinical issues that might inform treatment decision making in routine clinical practice (eg, drug overuse headache or potential withdrawal symptoms). Additionally, because of the paucity of information reported in the original studies, we were not able to quantify some outcomes, such as global functioning.

Clinical and policy implications

Results on both benefits and harms should inform shared clinical decision making, considering the preferences of patients, caregivers, and healthcare professionals. Our findings should help inform future guidelines and updates to recommendations to ensure that patients receive optimal care. Overall, the results of our network meta-analysis suggest that the best performing triptans should be considered the treatment of choice for migraine episodes owing to their capacity for inducing rapid and sustained pain freedom, which is of key importance for people with migraine. 50 While the recent introduction of lasmiditan, rimegepant, and ubrogepant has expanded options for the acute treatment of migraine, the high cost of these newer drugs, along with the substantial adverse effects of lasmiditan, suggest their use as third line options, after the less expensive, similarly efficacious, second line options such as ibuprofen, acetylsalicylic acid, diclofenac potassium, almotriptan, and frovatriptan have been considered. However, ranking of treatments in clinical guidelines extends beyond efficacy, tolerability, safety, and acquisition costs alone and must also consider cost effectiveness, of which analyses are warranted, and accessibility. The inclusion of the most effective triptans (available as generic drugs) into the WHO Model List of Essential Medicines should be considered to promote global accessibility and uniform standards of care (currently, sumatriptan is the only triptan included). 39 Limited access to triptans and their substantial underutilisation represents missed opportunities to offer more effective treatments and deliver better quality of care to people who experience migraine. 3

Conclusions

The results of this systematic review and network meta-analysis offer the best available evidence to guide the choice of acute oral drug interventions for migraine episodes. Our results are in line with recent observational evidence. 51 Careful comparisons between randomised controlled trials and observational evidence represent a productive line of research, as they may complement one another, and both can inform clinical decision making. 52 Nevertheless, we believe that, making the best use of the available, if limited, randomised evidence, our results and tools are valid and should be used to guide treatment choices, promoting shared, informed decision making between patients and clinicians.

All the statements comparing the performance of one drug with another should be tempered by the potential limitations of the current analyses, the quality of the available evidence, the characteristics of the study population, and the long term management of migraine. 53 Future network meta-analyses using individual patient data are required to improve personalised guidance for managing acute treatment of migraine episodes.

What is already known on this topic

Migraine is a highly prevalent condition and among the leading causes of disability worldwide

Numerous oral drugs with different mechanisms of action are available for the acute management of migraine, but no clear consensus exists among clinical guidelines about the ranking of these treatments

Previous systematic reviews and network meta-analyses have only included a subset of currently licensed drugs

What this study adds

Considering both efficacy and tolerability, eletriptan, rizatriptan, sumatriptan, and zolmitriptan showed the best overall performance for the acute treatment of migraine

Eletriptan, rizatriptan, sumatriptan, and zolmitriptan were more efficacious than the recently marketed and more expensive drugs lasmiditan, rimegepant, and ubrogepant, which showed efficacy comparable to paracetamol and most non-steroidal anti-inflammatory drugs

Triptans are currently widely underused, and access to the most effective triptans should be promoted globally and international guidelines updated accordingly

Ethics statements

Ethical approval.

Not required.

Data availability statement

The full dataset and information for the vitruvian plots are freely available online at GitHub ( https://github.com/EGOstinelli/NMA-on-migraine/ ).

Acknowledgments

We express our gratitude to the representatives of international patient organisations who helped to interpret the results and provided feedback on the manuscript: Kylie Petrarca (US), Louise Houle (Canada), and Mariá Agustina Hildt (Argentina). We also acknowledge Lori Meador for providing unpublished supplementary trial data.

Contributors: WKK, EGO, HA, HCD, AC, and MA conceived and designed the study. WKK, EGO, HA, ERT, HCD, AC, and MA contributed to the methods of the study. WKK, ZAZ, LK, RHC, HMA, and CID selected the articles and extracted the data. WKK, EGO, and AC analysed the data. EGO, AT, and AC accessed and verified the data. WKK, EGO, HA, HCD, AC, and MA wrote the first draft of the manuscript. All authors interpreted the data and contributed to the writing of the final version of the manuscript. All authors agreed with the results and conclusions of this manuscript and had full access to all the data. WKK and EGO are joint first authors. AC and MA are joint last authors and are responsible for the decision to submit for publication. They are the guarantors. The corresponding author attests that all listed authors meet authorship criteria and that no others meeting the criteria have been omitted.

Funding: This study was funded by the National Institute for Health and Care Research (NIHR) Oxford Health Biomedical Research Centre (NIHR203316) and the Lundbeck Foundation professor grant (R310-2018-3711). The views expressed are those of the authors and not necessarily those of the UK National Health Service, NIHR, UK Department of Health, or Lundbeck Foundation. The funders of the study had no role in study design, data collection, data analysis, data interpretation, writing of the report, or in the decision to submit for publication.

Competing interests: All authors have completed the ICMJE uniform disclosure form at www.icmje.org/disclosure-of-interest/ and declare: WKK has received an educational fee from Pfizer outside of the submitted work. EGO is supported by the National Institute for Health and Care Research (NIHR) Oxford Health Biomedical Research Centre (NIHR203316) and the Lundbeck Foundation Applied Research Collaboration Oxford and Thames Valley at Oxford Health National Health Service Foundation Trust, by the NIHR Oxford Cognitive Health Clinical Research Facility, by the NIHR Oxford Health Biomedical Research Centre, by the Brasenose College Senior Hulme Scholarship, and has also received research and consultancy fees from Angelini Pharma. ZAZ has received a scholarship grant from Rigshospitalet. LK has received a research grant from the Lundbeck Foundation (R155–2014–171). RHC has received support for travel from the Augustinus Foundation. HMA have received an educational fee from Pfizer outside of the submitted work. CID has received an International Headache Society research fellowship grant, a Hellenic Neurology Society scholarship, support for travel from Merck Serono, and is a member of the European Headache Federation. AT has received research and consultancy fees from Angelini Pharma, INCiPiT (Italian Network for Paediatric Trials), and Takeda; and has also acted as a Clinical Advisor to Akrivia Health. HA reports personal fees from Lundbeck, Pfizer, and Teva outside of the submitted work. ERT is the current executive director and the past president of the European Migraine and Headache Alliance. HCD received honorariums for participation in clinical trials, contribution to advisory boards or oral presentations from: AbbVie, Lilly, Lundbeck, Novartis, Pfizer, Teva, Weber & Weber, and WebMD. The German Research Council (DFG) and the German Ministry of Education and Research (BMBF) support headache research by HCD. HCD serves on the editorial boards of Cephalalgia, Lancet Neurology, and Drugs. AC is supported by the NIHR Oxford Cognitive Health Clinical Research Facility, by an NIHR Research Professorship (grant RP-2017-08-ST2-006), by the NIHR Oxford and Thames Valley Applied Research Collaboration, by the NIHR Oxford Health Biomedical Research Centre (grant NIHR203316), and by the Wellcome Trust (GALENOS Project); AC has also received research, educational, and consultancy fees from INCiPiT (Italian Network for Paediatric Trials), CARIPLO Foundation, Lundbeck, and Angelini Pharma. MA is a consultant, speaker, or scientific advisor for AbbVie, Amgen, Astra Zeneca, Eli Lilly, GlaxoSmithKline, Lundbeck, Novartis, Pfizer, and Teva; a primary investigator for ongoing AbbVie and Pfizer trials; and is the past president of the International Headache Society; MA is supported through the Lundbeck Foundation professor grant (R310-2018-3711) and serves as associate editor of the Journal of Headache and Pain , and associate editor of Brain .

Transparency: The lead authors (AC and MA) affirm that the manuscript is an honest, accurate, and transparent account of the study being reported; that no important aspects of the study have been omitted; and that any discrepancies from the study as planned (and, if relevant, registered) have been explained.

Dissemination to participants and related patient and public communities: We plan to disseminate the results to relevant patient communities through the media relations department of our institutions. We also plan to use social media, as well as the websites of our organisations and societies involved in research and treatment of headache and migraine.

Provenance and peer review: Not commissioned; externally peer reviewed.

This is an Open Access article distributed in accordance with the terms of the Creative Commons Attribution (CC BY 4.0) license, which permits others to distribute, remix, adapt and build upon this work, for commercial use, provided the original work is properly cited. See: http://creativecommons.org/licenses/by/4.0/ .

• Abbafati C ,
• GBD 2019 Diseases and Injuries Collaborators
• Katsarava Z ,
• Ferrari MD ,
• Goadsby PJ ,
• Burstein R ,
• Robbins MS ,
• Board of Directors of the American Headache Society
• de Gaalon S ,
• ↵ Diener HC, Forderreuther S, Kropp P. Treatment of migraine attacks and preventive treatment of migraine, S 1 guideline, 2022, DGN and DMKG. Dtsch Ges Für Neurol Pub . Published online October 12, 2023:1-212. https://ihs-headache.org/wp-content/uploads/2023/06/DMKG_Treatment-of-migraine-attacks-and-preventive-treatment-of-migraine-2022.pdf
• Schytz HW ,
• Jensen RH ,
• Petersen CL ,
• Hougaard A ,
• ↵ Higgins J, Thomas J, Chandler J, et al. Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). www.training.cochrane.org/handbook
• Cameron C ,
• Johnston K ,
• Deighton A ,
• Peres MFP ,
• Scala WAR ,
• Polavieja P ,
• Venkata SK ,
• Wilhelm S ,
• Johansson E
• Puledda F ,
• Huessler EM ,
• Salanti G ,
• Caldwell DM ,
• Headache Classification Committee of the International Headache Society
• Headache Classification Committee of the International Headache Society (IHS)
• Kelley NE ,
• Sterne JAC ,
• Savović J ,
• Diener HC ,
• Tassorelli C ,
• Dodick DW ,
• International Headache Society Clinical Trials Standing Committee
• Cipriani A ,
• Higgins JP ,
• Geddes JR ,
• Hugger SS ,
• Chalmer MA ,
• Kogelman LJA ,
• Callesen I ,
• DBDS Genomic Consortium
• Silberstein SD
• Barrett JK ,
• Jackson D ,
• Higgins JPT
• Veroniki AA ,
• Vasiliadis HS ,
• Efthimiou O ,
• Schwarzer G ,
• Higgins JPT ,
• Ostinelli EG ,
• ↵ World Health Organization. World Health Organization Model List of Essential Medicines, 23rd list. 2023. https://www.who.int/publications/i/item/WHO-MHP-HPS-EML-2023.02
• Nikolakopoulou A ,
• Papakonstantinou T ,
• VanderPluym JH ,
• Halker Singh RB ,
• Urtecho M ,
• Herberhold J ,
• Lipton RB ,
• Nicholson RA ,
• Tarnutzer AA ,
• Robinson KA ,
• Newman-Toker DE
• Liberman AL ,
• ↵ ClinicalTrials.gov. NCT05509400 . 2022. https://clinicaltrials.gov/study/NCT05509400
• Hróbjartsson A ,
• Forfang E ,
• Altman DG ,
• Gøtzsche PC
• Furukawa TA ,
• De Crescenzo F ,
• Smelt AFH ,
• Louter MA ,
• Chiang CC ,
• Horvath Z ,
• Sheldrick RC
• Hovaguimian A ,

Trump's claims of a migrant crime wave are not supported by national data

WASHINGTON — When Donald Trump speaks at the southern border in Texas on Thursday, you can expect to hear him talk about “migrant crime,” a category he has coined and defined as a terrifying binge of criminal activity committed by undocumented immigrants spreading across the country.

“You know, in New York, what’s happening with crime is it’s through the roof, and it’s called ‘migrant,’” the former president said at a rally in Michigan earlier this month. “They beat up police officers. You’ve seen that they go in, they stab people, hurt people, shoot people. It’s a whole new form, and they have gangs now that are making our gangs look like small potatoes.”

Trump has undoubtedly tapped into the rising anger over crimes allegedly committed by undocumented migrants that have gained national attention — most recently, the killing of college student Laken Riley in Georgia last week, after which an undocumented migrant from Venezuela was arrested and charged with her murder, and the much-reported fight between New York police officers and a group of migrant teens.

According to a recent Pew  poll , 57% of Americans said that a large number of migrants seeking to enter the country leads to more crime. Republicans (85%) overwhelmingly say the migrant surge leads to increased crime in the U.S. A far smaller share of Democrats (31%) say the same. The poll found that 63% of Democrats say it does not have much of an impact.

But despite the former president’s campaign rhetoric, expert analysis and available data from major-city police departments show that despite several horrifying high-profile incidents, there is no evidence of a migrant-driven crime wave in the United States.

That won’t change the way Trump talks about immigrants in his bid to return to the White House, as he argues that President Joe Biden’s immigration policies are making Americans less safe. Trump says voters should hold Biden personally responsible for every crime committed by an undocumented immigrant.

An NBC News review of available 2024 crime data from the cities targeted by Texas’ “Operation Lone Star,” which buses or flies migrants from the border to major cities in the interior — shows overall crime levels dropping in those cities that have received the most migrants.

Overall crime is down year over year in  Philadelphia ,  Chicago , Denver ,  New York  and Los Angeles. Crime has risen in  Washington, D.C ., but local officials do not attribute the spike to migrants.

“This is a public perception problem. It’s always based upon these kinds of flashpoint events where an immigrant commits a crime,” explains Graham Ousey, a professor at the College of William & Mary and the co-author of “Immigration and Crime: Taking Stock.” “There’s no evidence for there being any relationship between somebody’s immigrant status and their involvement in crime.”

Ousey notes the emotional toll these incidents have taken and how they can inform public perception, saying, “They can be really egregious acts of criminality that really draw lots of attention that involve somebody who happens to be an immigrant. And if you have leaders, political leaders who are really pushing that narrative, I think that would have the tendency to sort of push up the myth.”

“At least a couple of recent studies show that undocumented immigrants are also not more likely to be involved in crime,” Ousey says — in part because of caution about their immigration status. “The individual-level studies actually show that they’re less involved than native-born citizens or second-generation immigrants.”

Another misconception often cited by critics is that crime is more prevalent in “sanctuary cities.” But a Department of Justice report found that “there was no evidence that the percentage of unauthorized or authorized immigrant population at the city level impacted shifts in the homicide rates and no evidence that immigration is connected to robbery at the city level.”

Trump’s campaign claims without evidence that those statistics obscure the problem.

“Democrat cities purposefully do not document when crimes are committed by illegal immigrants, because they don’t want American citizens to know the truth about the dangerous impact Joe Biden’s open border is having on their communities,” Karoline Leavitt, Trump campaign press secretary, said in a statement. “Nevertheless, Americans know migrant crime is a serious and growing threat; and the murder, rape, or abuse of one innocent citizen at the hands of an illegal immigrant is one too many.”

Trump has been pushing the argument that immigrants bring crime since launching his first campaign in 2015, often featuring at his rallies the family members of those who were killed by undocumented immigrants who had been drinking and driving. And his arguments are not new — opponents of immigration have long tried to make the case that migrants bring crime.

National crime data, especially pertaining to undocumented immigrants, is notoriously incomplete. The national data comes in piecemeal and can only be evaluated holistically when the annual data is released.

The data is incomplete on how many crimes each year are committed by migrants, primarily because most local police don’t record immigration status when they make arrests. But the studies that have been done on this, most recently by the University of Wisconsin-Madison, show that in Texas, where police do record immigration status, migrants commit fewer crimes per capita.

In December 2020, researchers studying Texas crime statistics found that “contrary to public perception, we observe considerably lower felony arrest rates among undocumented immigrants compared to legal immigrants and native-born U.S. citizens and find no evidence that undocumented criminality has increased in recent years.”

Olympia Sonnier is a field producer for NBC News. 

Garrett Haake is NBC News' senior Capitol Hill correspondent. He also covers the Trump campaign.