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• 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

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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.

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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

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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.

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

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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.).

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Correspondence to Denny Borsboom .

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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.

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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

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• v.6(1); 2018

Network analysis: a brief overview and tutorial

David hevey.

School of Psychology, Trinity College Dublin, Dublin, Ireland

Objective : The present paper presents a brief overview on network analysis as a statistical approach for health psychology researchers. Networks comprise graphical representations of the relationships (edges) between variables (nodes). Network analysis provides the capacity to estimate complex patterns of relationships and the network structure can be analysed to reveal core features of the network. This paper provides an overview of networks, how they can be visualised and analysed, and presents a simple example of how to conduct network analysis in R using data on the Theory Planned Behaviour (TPB).

Method : Participants ( n  = 200) completed a TPB survey on regular exercise. The survey comprised items on attitudes, normative beliefs, perceived behavioural control, and intentions. Data were analysed to examine the network structure of the variables. The EBICglasso was applied to the partial correlation matrix.

Results : The network structure reveals the variation in relationships between the items. The network split into three distinct communities of items. The affective attitude item was the central node in the network. However, replication of the network in larger samples to produce more stable and robust estimates of network indices is required.

Conclusions : The reported network reveals that the affective attitudinal variable was the most important node in the network and therefore interventions could prioritise targeting changing the emotional responses to exercise. Network analysis offers the potential for insight into structural relations among core psychological processes to inform the health psychology science and practice.

Introduction

Health psychology research examines how the complex interactions between biological, psychological, and social factors influence health and well-being. For example, the UK Foresight map of obesity (see https://www.gov.uk/government/collections/tackling-obesities-future-choices ) provides a comprehensive representation of the complex system of over 300 relationships between over 100 variables and obesity (Finegood, Merth, & Rutter, 2010 ). The developers of the map assumed that obesity is the result of the interplay between a wide variety of factors, including a person’s physical make-up, eating behaviour, and physical activity pattern. The system reflects the relevant factors and their interdependencies that produce obesity as a behavioural outcome. The variables were classified into various categories of causal factors; for example, social psychological factors (e.g. peer pressure), individual psychological factors (e.g. stress), environmental factors (e.g. the extent to which one’s environment makes it easy to engage in regular walking), and individual physical activity factors (e.g. functional fitness). On the basis of expert academic opinion the Foresight report authors proposed that the variables in the system not only influence obesity, but can also have positive (e.g. high levels of stress cause high levels of alcohol consumption) and negative (e.g. high levels of stress cause low levels of physical activity) effects on each other, some have distal effects whereas others have proximal effects, and effects can be unidirectional (e.g. social attitudes towards fatness causes conceptualisations of obesity as an illness) or reciprocal (e.g. physical activity causes functional fitness, which causes physical activity). Networks are a fundamental characteristic of such complex systems; consequently, health psychological science can benefit from considering the network structure of the phenomena that it seeks to understand. It has been argued that networks pervade all aspects of human psychology (Borgatti, Mehra, Brass, & Labianca, 2009 ), and in the past decade network analysis has become an important conceptual and analytical approach in psychological research. Although network analysis has a long history of being applied in causal attribution research (e.g. Kelly, 1983 ) and social network analysis (Clifton & Webster, 2017 ), its broader potential for psychological science was highlighted over a decade ago by van der Maas et al. ( 2006 ). The frequently reported patterns of positive correlations between various cognitive tasks (e.g. verbal comprehension and working memory) are typically explained in terms of a dominant latent factor, i.e. the correlations reflect a hypothesised common factor of general intelligence ( g ). However, van der Maas and colleagues argued that this empirical pattern can also be accounted for by means of a network approach, wherein the patterns of positive relationships can be explained using a mutualism model, i.e. the variables have mutual, reinforcing, relationships. From a network analysis perspective, the network of relationships between the variables constitute the psychological phenomenon (De Schryver, Vindevogel, Rasmussen, & Cramer, 2015 ), which is a system wherein the constituent variables mutually influence each other without the need to hypothesise the existence of causal latent variables (Schmittmann et al., 2013 ). In addition to addressing psychometric issues (Epskamp, Maris, Waldorp, & Borsboom, In Press ) network perspectives can inform other areas of psychological science.

A key impetus for the current research on networks in psychology derives from Borsboom and colleagues’ influential application of networks in the field of clinical psychology in relation to psychopathology symptoms (e.g. Borsboom, 2017 ; Borsboom & Cramer, 2013 ; Cramer et al., 2016 ; Cramer, Waldorp, van der Maas, & Borsboom, 2010 ). Network models are also increasingly applied in other areas such as health related quality of life (HRQOL) assessment in health psychology (e.g. Kossakowski et al., 2016 ), personality (e.g. Costantini et al., 2015 ; Mõttus & Allerhand, 2017 ), and attitudes (e.g. Dalege et al., 2015 ). The psychosystems research team (i.e. Denny Borsboom, Angélique Cramer, Sacha Epskamp, Eiko Fried, Don Robinaugh, Claudia van Borkulo, Lourens Waldorp, Han van der Maas) are critical innovators for network analysis in psychology and this paper draws extensively from the key papers from the team and their collaborators; the psychosystems.org webpage is an essential resource for anyone interested in network analysis theory, process and applications.

To date, network analysis has not been widely applied in health psychology; however, network models are particularly salient for health psychology because many of the psychological phenomena we seek to understand are theorised to depend upon a large number of variables and interactions between them. The biopsychosocial model (e.g. Engel, 1980 ) has underpinned health psychology research and theory for the past 4 decades, and it reflects a complex system of mutually interacting and dynamic biological, psychological, interpersonal, and contextual effects on health (Lehman, David, & Gruber, 2017 ; Suls & Rothman, 2004 ). From a network perspective, health behaviours and outcomes can be conceptualised as emergent phenomena from a system of reciprocal interactions: network analysis offers a powerful methodological approach to investigate the complex patterns of such relationships. The overall global structural organisation, or topology, of the phenomenon and the roles played by specific variables in the network can be analysed in a manner that other statistical approaches cannot provide. In general, health psychology research, like many areas of psychology, has studied aspects of systems in isolation: for example, using regression models to examine the relationship between focal beliefs and moods and a specific outcome such as health behaviours or adaptation to illness. Although such research provides important insights, this approach is not suited for examining complex systems of interconnected variables and it does not help us easily piece back the various separate research findings on discrete components/sub-pathways into the more complex and complete system. As noted above, the complex interplay of physiological, psychological, social and environmental factors have been highlighted in the context of obesity. Comparable exercises for other chronic illnesses will produce similarly complex networks of variables. Network analysis provides a means to understand system-level relationships in a manner that can enhance psychological science and practice.

Health psychology research often focuses on HRQOL as a key outcome variable and HRQOL is frequently understood as being the common effect of observed items in scales, e.g. increased daily pain causes lower mental health. Network analysis has been applied to the SF-36 (Ware & Sherbourne, 1992 ), a widely used HRQOL scale, to examine the patterns of relationships between the items: Kossakowski et al. ( 2016 ) found that the observed covariances between the items may result largely from direct interactions between items. From this perspective, HRQoL emerges from a network of mutually interacting characteristics; the specific nature of the interacting relationships (e.g. causal effect, bidirectional effect, or effects of unmodelled latent variables) requires additional clarification. In addition to offering novel insights into psychometrics, a network approach can be applied to other important health psychology variables (e.g. illness representations, coping strategies) to better understand the nature of the relationships between items used in measurement.

Borsboom’s research on the networks of patterns of interconnected relationships between symptoms of various psychiatric disorders has resulted in the development of a novel network theory of mental disorders (Borsboom, 2017 ). This theory provides new insights into how trigger events can activate pathways in strongly connected networks to produce symptoms that can become self-sustaining, i.e. because the symptoms are strongly connected, feedback relations between them mean that they can activate each other after the triggering event has been removed. The absence of the trigger may be not be sufficient to de-activate the symptom network and return the person to a state of health; such insights from a network theory of psychopathology can help inform not only understandings of how and why symptoms are maintained, but also how such networks can be targeted to help transition the network back into a healthy state. Of note, such an approach may be beneficial for health psychology approaches to understanding clusters of symptom presentations over time in conditions such as chronic pain and chronic fatigue syndrome.

The network structures of individuals can be visualised and analysed; consequently we may be able to see how the system of beliefs, emotional states, behaviours and symptoms influence each other over time. Systems might comprise sets of variables that are diverse and only marginally connected, or could consist of variables that are highly interconnected. Understanding an individual’s personalised network may allow insight into when an individual’s specific patterns of beliefs and behaviours reach a tipping point, which then negatively impact on mood and symptoms. Such system transitions (e.g. moving from a state of wellness to being impaired functionally) occur gradually in response to changing conditions or they may be triggered by an external perturbation, e.g. life stressor. An individual may have a very robust network so that it remains stable despite the perturbations (e.g. symptom flare up) and consequently the person can maintain function, whereas other individuals may have less resilient networks wherein it is challenging to restore disturbed equilibrium. How such networks evolve over time and respond to changes in key and peripheral variables cannot be understood using traditional analytical methods: network analysis offers rich potential to further our understanding of complex systems of relationships among variables.

The Causal Attitude Network (CAN) model, which conceptualises attitudes as networks of causally interacting evaluative reactions (i.e. beliefs, feelings, and behaviours towards an attitude object; Dalege et al., 2015 ), is also of particular interest to health psychologists given the centrality of attitudinal variables in many core psychological models (e.g. Theory of Planned Behaviour, Health Belief Model). The capacity to graphically visualise complex patterns of relationships further offers the potential for insight into the salient psychological processes and to highlight theoretical gaps. For example, Langley, Wijn, Epskamp, and Van Bork ( 2015 ) used network analysis to examine the Health Belief Model variables in relation to girls’ intentions to obtain HPV vaccination. They reported that although some aspects of the HBM (e.g. perceived efficacy) were related to intentions, other core constructs such as cues to action were less relevant. In addition, social factors, currently not included in the HBM, were important in the network; such research can inform conceptual developments linking individual beliefs with social context to better understand healthy behaviours. Consequently, the network approach offers the potential to gain novel insights as the network structure can be analysed to reveal both core structural and relational features.

The aim of this paper is to provide an overview of networks, how they can be visualised and analysed, and to present a simple example of how to conduct network analysis on empirical data in R (R Core Team, 2017 ).

What is a network?

At an abstract level, a network refers to various structures comprising variables, which are represented by nodes, and the relationships (formally called edges ) between these nodes. For example, from the Foresight Report the variables such as stress, peer pressure, functional fitness, nutritional quality of food and drink represent nodes in the network, and the positive and negative relationships between those nodes are edges. There are some differences in nomenclature in the network literature: nodes are sometimes referred to as vertices, edges are sometimes referred to as links, and networks are also called graphs. Networks can be estimated based on cross-sectional or longitudinal time-series data; in addition, networks can be analysed at the group or individual level. Cross sectional data from a group can reveal group-level conditional independence relationships (e.g. Rhemtulla et al., 2016 ). Individualised networks based on times series data can provide insights into a specific individual over time (e.g. Kroeze et al., 2017 ). Furthermore, the networks produced by different populations can be compared. In general, network analysis represents a wide range of analytical techniques to examine different network models.

In psychological networks, nodes represent various psychological variables (e.g. attitudes, cognitions, moods, symptoms, behaviours), while edges represent unknown statistical relationships (e.g. correlations, predictive relationships) that can be estimated from the data. A node can represent a single item from a scale, a sub-scale, or a composite scale: the choice of node depends upon the type of data that provide the most appropriate and useful understanding of the questions to be addressed. Edges can represent different types of relationships, e.g. co-morbidity of psychological symptoms, correlations between attitudes.

Two types of edges can be present in a network: (1) a directed edge: the nodes are connected and one head of the edge has an arrowhead indicating a one-way effect, or (2) an undirected edge: the nodes have a connecting line indicating some mutual relationship but with no arrowheads to indicate direction of effect. Networks can be described as being directed (i.e. all edges are directed) or undirected (i.e. no edges are directed). For example, edge direction has been used in psychology networks particularly for representing cross-lagged relationships among variables (Bringmann et al., 2016 ). A directed network can be cyclic (i.e. we can follow the directed edges from a given node to end up back at that node) or acyclic (i.e. you cannot start at a node and end up back at that node again by following the directed edges).

Directed networks can represent causal structures (Pearl, 2000 ); however, such directed networks can have very strict assumptions, i.e. all the variables that have a causal effect are measured in the network, and the causal chain of cause and effect is not cyclic (i.e. a variable cannot cause itself via any path) (Epskamp, Borsboom, & Fried, 2018a ). Although Directed Acyclic Graphs (DAGs) have been frequently reported in the epidemiological research literature in the past two decades (Greenland, Pearl, & Robins, 1999 ), the acyclic assumption may be untenable in many contexts for psychology. For example, in many psychological phenomena, reciprocal effects may exist between variables: having a positive attitude towards a behaviour results in that behaviour, which then results in a more positive attitude. In addition, directed networks suffer from the problem, similar to that arising in Structural Equation Modelling, that many equivalent models can account for the pattern of relationships found in the data (Bentler & Satorra, 2010 ; MacCallum, Wegener, Uchino, & Fabrigar, 1993 ). In their recent review of the challenges for network theory and methodology in psychopathology, Fried and Cramer ( 2017 ) note that despite the plausibility of many causal psychopathological symptom pathways in networks, there is a need to build stronger cases for the causal nature of these relationships. They highlight that many network papers have estimated undirected networks in cross-sectional data, and that even those that use directed networks based on time-series data at best show that variables measured at one moment in time can predict another variable at a different measurement time ( Granger causality ; Granger, 1969 ), which satisfies the requirement for putative causes preceding their effects (Epskamp et al., 2018b ). Although such a temporal relationship may indicate a causal relationship, it is possible that the link may occur for other reasons (e.g. a unidimensional autocorrelated factor model would lead to every variable predicting every other variable over time; Epskamp et al., 2018b ). Spirtes, Glymour, and Scheines ( 2000 ) developed the PC algorithm, which can be used to examine networks to find candidate causal structures that may have generated the observed patterns of relations present. However, such approaches have not been widely used to date in psychological networks. In general, network analysis can be considered as hypothesis-generating for putative causal structures that require empirical validation.

Edges convey information about the direction and strength of the relationship between the nodes. The edge may be positive (e.g. positive correlation/covariance between variables) or negative (e.g. negative correlation/covariance between variables); the polarity of the relationships is represented graphically using different coloured lines to represent the edges: positive relationships are typically coloured blue or green, and negative relationships are coloured red. Edges can be either weighted or unweighted . A weighted edge reflects the strength of the relationship between nodes by varying the thickness and colour density of the edge connecting the nodes: thicker denser coloured lines indicate stronger relationships. Alternatively, the edge may be unweighted and simply represent the presence vs . absence of a relationship; in such a network, the absence of a relationship results in the nodes not having a connecting edge.

Figure 1 presents a simple network model representing the partial correlation matrix between 5 variables (A - E) below ( Table 1 ). The size and colour density of the lines (edges) vary to reflect the varying strength of relationship between the variables; the edges are non-directional as the data represented as bivariate partial correlations between the variables. The network comprises both positive (green lines) and negative correlations (red lines) between the variables. Some variables are more central and have more connections than others: C relates to all the variables in the network, whereas D only relates to two other variables.

Sample network with 5 nodes and 8 edges. Postive edges are green and negative edges are red. The numbers represent the correlations between the variables.

Having briefly outlined the basic features of a network, the next sections will outline the three core analytical steps in network analysis:

• Estimate the network structure based on a statistical model that reflects the empirical patterns of relationships between the variables
• Analyse the network structure
• Assess the accuracy of the network parameters and measures.

1. Estimating the Network

Historically, network science has developed using graphical approaches to represent relationships between nodes. For example, Leonhard Euler’s application of ‘geometry of position’, Gustav Kirchoff’s work on the algebra of graphs in relation to electrical networks, and Cayley’s contributions to molecular chemistry all utilised graphical approaches to network data (Estrada & Knight, 2015 ). The network visually represents the pattern of relationships between variables and a network can be estimated using common statistical parameters that quantify relationships, e.g. correlations, covariances, partial correlations, regression coefficients, odds ratios, factor loadings. However, as correlation networks can contain spurious edges, for example due to an (unmeasured) confounding variable, the most common approach in psychology uses partial correlations to create the relationships between variables. For example, if we had a network examining the relationship between risk behaviours (e.g. caffeine consumption) and health outcome (e.g. cancer), the analysis would show a relationship between the variables; however, such a relationship may simply reflect the fact that an unmeasured confound (e.g. smoking) is associated with both caffeine consumption and cancer. Partial correlations, similar to multiple regression coefficients, provide estimates of the strength of relationships between variables controlling for the effects of the other measured variables in the network model. Thus it is critically important to measure such potential confounding variables to ensure that their effects are controlled for. Two nodes are connected if there is covariance between those nodes that cannot be explained by any other variable in the network. The resulting partial correlations not only provide an estimate of the direct strength of relationships, but can also indicate mediation pathways: in Figure 1 A and D are not directly connected (i.e. no edge between them) but A influences C, which in turn influences D, thus C mediates the relationship between A and D. Partial correlation networks can provide valuable hypothesis generating structures, which may reflect potential causal effects to be further examined in terms of conditional independence (Pearl, 2000 ).

As noted previously, undirected network models in psychology have typically been examined, and a frequently used model in estimating such networks is the pairwise Markov Random Field (PMRF), which is a broad class of statistical models. A PMRF model is characterised by undirected edges between nodes that indicate conditional dependence relations between nodes. An absent edge means that two nodes are conditionally independent given all other nodes in the network. An edge indicates conditional dependence given all other nodes in the network. Different PMRF models can be used, depending upon the type of data (continuous, ordinal, binary, or mixtures of these data types) to be modelled. When continuous data are multivariate normally distributed, analysing the partial correlations using the Gaussian graphical model (GGM; Costantini et al., 2015 ; Lauritzen, 1996 ) is appropriate. If the continuous data are not normally distributed then a transformation (e.g. nonparanormal transformation, Liu, Lafferty, & Wasserman, 2009 ) can be applied prior to applying the GGM. The GGM can also be used for ordinal data, wherein the network is based on the polychoric correlations instead of partial correlations (Epskamp, 2018 ). If all the research variables are binary, the Ising Model can be used (van Borkulo et al., 2014 ). When the data comprise a mixture of categorical and continuous variables, the Mixed Graphical Model can be used to estimate the PMRF (Haslbeck & Waldorp, 2016 ). Thus, networks can be estimated from various types of data in a flexible manner.

The network complexity requires consideration. The higher the number of nodes being examined, then the higher the number of edges have to be estimated: in a network with five nodes, 10 unique edges are estimated, whereas in a network with 10 nodes, 45 edges are estimated, and in a network with 20 nodes, 190 edges are estimated. In addition, in the case of an Ising model not only are edge weights estimated but so too are thresholds: in the case of 20 nodes that would mean an additional 20 parameters to be estimated. However, as mentioned above many of these edges (e.g. correlations) may be spurious, and an increase in the number of nodes can lead to over-fitting and very unstable estimates (Babyak, 2004 ). Like all statistical techniques that use sample data to estimate parameters, the correlation and partial correlations values will be influenced by sample variation and therefore exact zeros will be rarely observed in the matrices. Consequently, correlation networks will nearly always be fully connected networks, possibly with small weights on many of the edges that reflect weak and potentially spurious partial correlations. Such spurious relationships will be problematic in terms of the network interpretation and will compromise the potential for network replication. In order to limit the number of such spurious relationships, a statistical regularisation technique, which takes into account the model complexity, is frequently used.

A ‘least absolute shrinkage and selection operator’ (LASSO; Friedman, Hastie, & Tibshirani, 2008 ) with a tuning parameter set by the researcher is applied to the estimation of the partial correlation networks. The LASSO performs well in the estimation of partial correlation networks (Fan, Feng, & Wu, 2009 ), and it results in some small weak edge estimates being reduced to exactly zero, resulting in a sparse network (Tibshirani, 1996 ). The LASSO yields a more parsimonious graph (fewer connections between nodes) that reflects only the most important empirical relationships in the data. Of note, the absence of an edge does not present evidence that the edge is in fact exactly zero (Epskamp, Kruis, Marsman, & Marinazzo, 2017 ). The goal of the LASSO is to exclude spurious relationship but in doing so, it may omit actual relationships. Although many variants of the LASO have been developed, the graphicalLASSO ( glasso , Friedman et al., 2008 ) is recommended both in terms of ease of implementation in specific analysis programmes but also its felxibility in terms of non-continuous data (Epskamp & Fried, In Press ). The edge may be absent from the network if the data are too messy and noisy to detect the true relationship, and quantifying evidence for edge weights being zero is an ongoing research issue (Wetzels & Wagenmakers, 2012 ). Simulation studies show that the LASSO has a low likelihood of false positives, which provides some confidence that an observed edge is indeed present in the network (Krämer, Schäfer, & Boulesteix, 2009 ). However, the specific nature of the relationship reflected in the edge is still uncertain, e.g. the edge could represent a direct causal pathway between nodes, or it could reflect the common effect of a (latent) variable not included in the network model.

As mentioned previously, the use of the LASSO requires setting a tuning parameter. The sparseness of the network produced using the LASSO depends upon the value the researcher sets tuning parameter (λ): the higher the λ value selected the more edges are removed from the network and its value directly influences the structure of the resulting network. The tuning parameter λ therefore needs to be carefully selected to create a network structure that minimises the number of spurious edges while maximising the number of true edges (Foygel & Drton, 2010 ). In order to ensure that the optimal tuning parameter is selected, a common method involves estimating a number of networks under different λ values. These different networks range from a completely full network where every node is connected to each other to an empty network where no nodes are connected. The LASSO estimates produce a collection of networks rather than a single network; the researcher needs to select the optimal network model and typically this is achieved by minimising the Extended Bayesian Information Criterion (EBIC; Chen & Chen, 2008 ), which has been shown to work particularly well in identifying the true network structure (Foygel & Drton, 2010 ; van Borkulo et al., 2014 ), especially when the true network is sparse. Model selection using the EBIC works well for both the Ising model (Foygel Barber & Drton, 2015 ) and the GGM (Foygel & Drton, 2010 ). The EBIC has been widely used in psychology networks (e.g. Beard et al., 2016 ; Isvoranu et al., 2017 ) and it enhances both the accuracy and interpretability of networks produced (Tibshirani, 1996 ).

The EBIC uses a hyperparameter ( γ ) that dictates how much the EBIC will prefer sparser models (Chen & Chen, 2008 ; Foygel & Drton, 2010 ). The γ value is determined by the researcher and is typically set between 0 and 0.5 (Foygel & Drton, 2010 ), with higher values indicating that simpler models (more parsimonious models with fewer edges) are preferred. In many ways the choice of γ depends upon the extent to which the researcher is taking a liberal or conservative approach to the network model. A value of 0 results in more edges being estimated, including possible spurious ones, but which can be useful in early exploratory and hypotheses generating research. Of note, a γ setting of zero will still produce a network that is sparser compared to a partial correlation network that has not be regularised using a LASSO. Although γ can be set at 1, the default in many situations is 0.5. Foygel and Drton ( 2010 ) suggest that setting the γ value 0.5 will result in fewer edges being retained, which will remove the spurious edges but it may also remove some other edges too. A compromise value γ of 0.25 is potentially a useful value to also use to see the impact on the network model produced.

Figure 2 presents the same data (questionnaire items on the big 5 model of personality, with 5 items for each dimension: Openness, Conscientiousness, Agreeableness, Extraversion, and Neuroticism) analysed using γ of 0, 0.5, and 0.99. With the tuning parameter set to 0, the network contains a dense array of connections as more edges are estimated; as the tuning parameter increases, the number of edges estimated decreases as the model become more sparse. This illustrates that the choices made by the researchers in setting the γ level will impact on the nature of the network produced. Of note, Epskamp and Fried ( In Press ) report that comparison of networks based on simulated data using γ of 0.00, 0.25 and 0.50 revealed the higher values of γ were able to reveal the true network structure but that the value of 0 included a number of spurious relationships. They caution that γ of .5 may still be conservative and not reflect the true model, and they note that the choice of γ is somewhat arbitrary and up to the researcher. Epskamp ( 2018 ) reported recently that increasing the γ to 0.75 or 1.00 did not outperform a γ of 0.5 in a well-established personality dataset.

Partial correlation networks estimated on same dataset, with increasing levels of the LASSO hyperparameter γ (from left to right: Panel (a) γ  = 0, Panel (b) γ  = 0.5, Panel (c) = 0.99).

In order to plot the network, the nodes and edges need to be positioned in manner that reflects the patterns of relationships present in the data. The most frequently used approach in psychological networks is the Fruchterman-Reingold algorithm (Fruchterman & Reingold, 1991 ), which calculates the optimal layout so that nodes with less strength and less connections are placed further apart, and those with more and/or stronger connections are placed closer to each other. The development of qgraph as a package to visualise patterns of relationships between nodes in networks was an invaluable contribution to advancing network analysis (Epskamp, Cramer, Waldorp, Schmittmann, & Borsboom, 2012 ).

2. Network Properties

After a network structure is estimated, the graphical representation of the network reveals the structural relationships between the nodes, and we can then further analyse the network structure in terms of its properties. This analysis provides insight into critically important features of the network. For example, are certain nodes more important (central) than others in the network? Is the global structure dense or sparse? Does it contain strong clusters of nodes (communities) or are the nodes isolated?

Not all nodes in a network are equally important in determining the network’s structure: centrality indices provide insight into the relative importance of a node in the context of the other nodes in the network (Borgatti, 2005 ; Freeman, 1978 ). For example, a central symptom is one that has a large number of connections in a network and its activity can spread activation throughout a symptoms network; in contrast, a peripheral symptom is on the outskirts of a network and has few connections and consequently less impact on the network. Different centrality indices provide insights into different dimensions of centrality. The indices can be presented as standardised z score indices to provide information on the relative importance of the nodes, and judging centrality requires careful consideration of the different dimensions in combination. These indices are based on the pattern of the connections in which the node of interest plays a role and can be used to model or predict several network processes, such as the amount of flow that traverses a node or the tolerance of the network to the removal of selected nodes (Borgatti, 2005 ). The most common aspects of centrality typically examined are as follows.

Degree : degree centrality is defined as the number of connections incident to the node of interest (Freeman, 1978 ).

Node strength : how strongly a node is directly connected to other nodes is based on the sum of the weighted number and strength of all connections of a specific node relative to all other nodes. Whilst degree provides information on the number of connections, strength can provide additional information on the importance of that node, for example a node with many weak connections (high degree) might not be as central to the network as one that has fewer but stronger connections. However, as noted by Opsahl, Agneessens, and Skvoretz ( 2010 ) merely focusing on node strength alone as an index of importance is potentially misleading as it does not take account of the number of other nodes to which it connected. Consequently, it is important to incorporate both degree and strength as indicators of the level of involvement of a node in the surrounding network when examining the centrality of a node. Opsahl et al. ( 2010 ) proposed the use of a degree centrality measure, which is the product of the number of nodes that a specific node is connected to, and the average weight of the edges to these nodes adjusted by an alpha ( α ) parameter, which determines the relative importance of the number of edges compared to edge weights. In combining both degree and strength, the tuning α parameter is set by the researcher: if this parameter is between 0 and 1, then having a high degree is regarded as favourable, whereas if it is set above 1, then a low degree is favourable.

Closeness : the closeness index quantifies the node’s relationship to all other nodes in the network by taking into account the indirect connections from that node. A high closeness index indicates a short average distance of a specific node to all other nodes; a central node with high closeness will be affected quickly by changes in any part of the network and can affect changes in other parts of the network quickly (Borgatti, 2005 ).

Betweenness : the betweenness index provides information on how important a node is in the average pathway between other pairs of nodes. A node can play a key role in the network if it frequently lies on the shortest path between two other nodes, and it is important in the connection that the other nodes have between them (Saramäki, Kivelä, Onnela, Kaski, & Kertész, 2007 ; Watts & Strogatz, 1998 ).

Clustering : the extent to which a node is part of a cluster of nodes can be estimated (Saramäki et al., 2007 ). The local clustering coefficient C is the proportion of edges that exist between the neighbours of a particular node relative to the total number of possible edges between neighbours (Bullmore & Sporns, 2009 ). It provides insight into the local redundancy of a node: does removing the node have an impact on the capacity of the neighbouring nodes to still influence each other? An overall global clustering coefficient (also referred to as transitivity) for the entire network can be estimated in both undirected and directed networks. Furthermore, the overall network may comprise communities , i.e. a clustering of nodes that are highly interconnected among themselves and poorly connected with nodes outside that cluster.

Detecting communities requires researchers to not simply interpret the placement of nodes in the visual representation of the data but to examine the patterns present using a formal statistical approach. Fried ( 2016 ) highlights a number of approaches to help identify communities. As latent variable models and network models are mathematically equivalent, examining the eigenvalues of components present in data using exploratory factor analysis is one way to identify how many communities might be present and the factor loadings indicate which nodes belong to which community. More sophisticated approaches include the spinglass algorithim (although this is limited by the fact that it often produces different results every time you run it, and it only allows nodes to be part of one community, whereas nodes may be better described as belonging to several communities at the same time), the walktrap algorithim (which provides more consistent results if you repeat it, but which also only allows nodes to be part of one community), and the Clique Percolation Method (CPM), which allows nodes to belong to more than one community (see Blanken et al., 2018 ).

Overall network topology

Networks can take on many different shapes; however, some common network shapes have been described in detail in the literature. Random networks comprise nodes with random connections, with each node have approximately the same number of connections to others. The distribution of the nodes’ connections follows a bell-curve. ‘Small world’ networks are characterised by relatively high levels of transitivity and nodes being connected to each other through small average path lengths (Watts & Strogatz, 1998 ). A classic example of the ‘small-world effect’ is the so-called ‘six degrees of separation’ principle, suggested by Milgram ( 1967 ). Letters passed from person to person reached a designated target individual in only a small (approximately 6) number of steps; the nodes (individuals) were connected by a short path through the network.

‘Scale free’ networks are characterised by a relatively small number of nodes that are connected to many other nodes (Barabási, 2012 ). These ‘hub’ nodes have an exceptionally high number of connections to other nodes, whereas the majority of non-hub nodes have very few connections. The distribution of the nodes’ connections follows a power law. Research has found that HIV transmission among men who have sex with men can be modelled as a scale free model (Leigh Brown et al., 2011 ); identifying individuals who are have very high levels of connections and represent ‘ superspreaders ’ of infections provides an efficient means for targeted vaccinations (Pastor-Satorras & Vespignani, 2001 ). Within scale free networks, nodes with high centrality measures and extremely higher centrality than other nodes may be ‘hubs’. However, it is critically important to check the pattern of directed relationships between the node and its neighbours, e.g. in a directed network a node could have a high centrality because it has many directed edges to other nodes (high OutDegree centrality) whilst having no edges from those nodes pointing at it (zero InDegree centrality); in this case the node would not be a hub. 1

In addition to group-level analysis, networks can be developed at a person-specific level: a time-series network of an individual may be useful for understanding the relationship between nodes (e.g. symptoms) at an individualised level, and could be used for personalised treatment planning (David, Marshall, Evanovich, & Mumma, 2018 ). If network structures are replicated and nodes emerge as hubs, then changing these hub nodes might have downstream effects on other nodes, which might result in an efficient means to change outcomes (Isvoranu et al., 2017 ). For example, network analysis may reveal that a certain belief is a hub and therefore critical in terms of impact on behaviour change: therefore we could focus our efforts on changing that belief rather than attempting to change multiple beliefs. Developing a better understanding of the structural relationships between the nodes in the network can provide important theoretical and practical insights for health psychology.

3. Network accuracy

As the network is based on sample data, the accuracy of the sample-based estimates of the population parameters reflecting the direction, strength and patterns of relationships between nodes should be considered. To-date much of the research on networks has used edge strength and node centrality to make inferences about the phenomenon being modelled. However, as Epskamp et al. ( 2018a ) note, relatively little attention has been paid towards examining the accuracy of the edge and centrality estimates. Given the relatively small sample sizes that typically characterises psychological research, edge strengths and node centrality may not be estimated accurately. Therefore, it is recommended that researchers determine the accuracy of both. The accuracy of edge weights is estimated by calculating confidence intervals (e.g. 95% CI) for their estimates. As a CI requires knowledge of the sampling distribution of the estimate, which may be difficult to obtain for the edge weight estimate, Epskamp et al. ( 2018a ) developed a method that uses bootstrapping (Efron, 1979 ) to repeatedly estimate a model under either sampled or simulated data, and then estimates the required statistic. The more bootstrap samples that are run, the more consistent the results. Either a parametric bootstrap or non-parametric bootstrap can be applied for edge-weights (Bollen & Stine, 1992 ). For non-parametric bootstrapping, observations in the data are resampled with replacement to create new plausible datasets. Parametric bootstrapping samples new observations from the parametric model that has been estimated from the original data; this creates a series of values that can be used to estimate the sampling distribution. Consequently, the parametric bootstrap requires a parametric model of the data whereas the non-parametric bootstrap can be applied to continuous, categorical and ordinal data. As the non-parametric bootstrap is data-driven and less likely to produce biased estimates with LASSO regularised edges (which tend to dominate in the literature), Epskamp et al. ( 2018a ) emphasise the usefulness and general applicability of the non-parametric bootstrap. If the bootstrapped CIs are wide, it becomes hard to interpret the strength of an edge.

The accuracy of the centrality indices can be examined by using a different type of bootstrapping: subsets of the data are used to investigate the stability of the order of centrality indices based on the varying sub-samples ( m out of n bootstrap; Chernick, 2011 ). The focus is on whether the order of centrality indices remains the same after re-estimating the network with less cases or nodes. A case-dropping subset bootstrap can applied and the correlation stability (CS) coefficient can quantify the stability of centrality indices using subset bootstraps. The correlation between the original centrality indices (based on the full data) is compared to the correlation obtained from the subset of data representing different percentages of the overall sample. For example, what is the correlation between the estimates from the entire data with the estimates based on a subset of 70% of the original sample? A series of such correlations can be presented to illustrate how the correlations change as the subset sample gets smaller (95% of the sample, 80%, 70%, … .25%). If the correlation changes considerably, then the centrality estimate may be problematic. A correlation stability coefficient of .7 or higher between the original full sample estimate and the subset estimates has been suggested as being a useful threshold to examine (Epskamp et al., 2018a ). A CS -coefficient (correlation = .7) represents the maximum proportion of cases that can be dropped, such that with 95 % probability the correlation between original centrality indices and centrality of networks based on subsets is 0.7 or higher (Epskamp et al., 2018a ). It is suggested that the CS -coefficient should not be below 0.25, and preferably it should be above 0.5.

Other applications of network analysis

The majority of research has examined networks based on cross-sectional data from a single group of participants. However, networks can also be determined for individuals over time as well as for comparing different groups. A network can be created for an individual based on time-series data to provide insights into that specific individual. Nodes that are identified as hubs in such networks could be important targets for interventions (Valente, 2012 ). Networks can be developed that model temporal effects between consecutive data measurements. The graphical VAR model (Wild et al., 2010 ) uses LASSO regularisation based on BIC to select the optimal tuning parameter (Abegaz & Wit, 2013 ). When multiple individuals are measured over time, multi-level VAR can be used and it estimates variation due to both time and to individual differences (Bringmann et al., 2013 ).

Networks can be estimated for different groups. Although the lack of methods comparing networks from different groups has been noted (Fried & Cramer, 2017 ), joint estimation of different graphical models (Danaher, Wang, & Witten, 2014 ; Guo, Levina, Michailidis, & Zhu, 2011 ) may prove useful in this context. For example the Fused Graphical Lasso (FGL) was recently used to compare the networks of borderline personality disorder patients with those from a community sample (Richetin, Preti, Costantini, De Panfilis, & Mazza, 2017 ). In addition, van Borkulo and colleagues have developed the Network Comparison Test (NCT) to allow researchers to conduct direct comparisons of two networks as estimated in different subpopulations (Van Borkulo, 2018 ). The test uses permutation testing in order to compare network structures that involve relationships between variables that are estimated from the data. The test focuses on the extent to which groups may differ in relation to (1) the structure of the network as a whole, (2) a given edge strength, (3) and the overall level of connectivity in the network. For example, research has reported that the network of MDD symptoms for those with persistent depression was more strongly connected than the network of those with remitting depression (van Borkulo et al., 2015 ).

Network analysis issues

Like all statistical models, the network model represents an idealised version of a real-world phenomenon that we wish to understand. In selecting the variables to be modelled we must decide which variables to include and how they are to be measured: each of these processes introduces error into the modelling process. A general concern for networks concerns their replicability (e.g. see Forbes, Wright, Markon, & Krueger, 2017 ; and responses by Borsboom et al., 2017 ; Steinley, Hoffman, Brusco, & Sher, 2017 ) and research needs to address this issue by estimating the stability of the networks and examining generalizability of the network model. As noted by Fried and Cramer ( 2017 ) the literature in general requires more conceptual and methodological developments for estimating both the accuracy and stability of networks. The identification of useful thresholds for these parameters will also prove critical in the interpretation of the network models. Similar to other methods of analysis (e.g. regression, SEM), network analysis is sensitive to the variables in the model and to the specific estimation methods used. Hence, the challenges regarding replication and generalizability are not unique to network modelling.

The larger the sample size, the more stable and accurately networks are estimated. Given the recent growth in use network analytic approaches in psychology it is not easy to hypothesise expected network structure and edge weights, which means there is little evidence to guide a priori power analyses. Epskamp et al. ( 2018a ) note that as more network research is conducted in psychology, more knowledge will accumulate regarding the nature of network structure and edge-weights that can be expected.

The dominant methods to date used to discover network structures in psychology are based on correlations, partial correlations, and patterns of conditional independencies. Further developments and application of causal model techniques will advance understanding of the relationships present in networks (Borsboom & Cramer, 2013 ). As noted previously, much of the research in psychological networks has been based on exploratory data analyses to generate networks; there is a need to progress towards confirmatory network modelling wherein hypotheses about network structure are formally tested.

How to run network analysis: an example using R

Many network structure analysis methods can be implemented in the generic software MATLAB and Stata, or specialised network software packages including UCINET (Borgatti, Everett, & Freeman, 2002 ) or Gephi ( https://gephi.org ). The Stanford Network Analysis Platform (SNAP) provides a network analysis library. R is an open-source statistical programming language that facilitates statistical analysis and data visualisation (R Core Team, 2017 ); to date much of the research on psychological networks has used R -packages igraph (Csárdi & Nepusz, 2006 ) or qgraph (Epskamp et al., 2012 ). Of note, the psychosystems research group has created specific R packages that make network analysis easier to implement (see psychosystems.org) . As mentioned at the start of this paper, their website is an essential resource for conducting network analysis in psychology. In this example, we will use the bootnet package as it provides a comprehensive suite of analytical options for network analysis. Data can inputted straight into R or can be imported in various common formats (e.g. csv. or txt. file) or from other data analysis programmes, e.g. Excel, SPSS, SAS and Stata.

R can be obtained via the https://www.r-project.org/ webpage. To download R , you need to select your preferred CRAN (Comprehensive R Archive Network) mirror ( https://cran.r-project.org/mirrors.html ). On the Mirrors webpage, you will find listings of countries that have identical versions of R and should select a location geographically close to your computer’s location. R can be downloaded for Linux, Windows, and Mac OS. The pages are regularly updated and you need to check with releases are supported for your platform. R as a base package can perform many statistical analyses but most importantly, R ’s functionality can be expanded by downloading specific packages.

After installing R ( https://www.r-project.org/ ), it is quite useful to also install R Studio ( https://www.rstudio.com/ ), which provides a convenient interface to R . Once both are installed, opening up R Studio will give a window that is split into 4 panes:

Console/Terminal : this pane is the main graphical interface for the user and this is where the commands are typed in.

Editor : this pane shows the active datasets that you are working on.

Environment/History/Connections : this pane shows the R datasets and allows you to import data from text (e.g. csv. file), Excel, SPSS, SAS and Stata. The History tab allows you see the list of your previous commands.

Files/plots/packages/help: this pane and its tabs can open files, view the most current plot (also previous plots), install and load packages, or use the general R help function.

Under the Tools drop down tap at the top of the R Studio screen, you can select which packages to install for the analyses required. Alternatively the packages can be installed using the Packages tab or they can be directly installed using a typed command. R is a command line driven programme and you can enter commands at the prompt (> by default) and each command is executed one at a time. For the current example, you will need to install 2 packages (‘ggplot2’ and ‘bootnet’) and the relevant command lines are:

>Install.packages("ggplot2")

>Install.packages("bootnet")

Once installed, the packages need to be loaded into R using the library("name of package") command.

>library("ggplot2")

>library("bootnet")

Next we need to tell R to import the data, in this case a csv. file called TPB2018.

The data are taken from a study conducted using the Theory of Planned Behaviour (TPB; Ajzen, 1985 , 2011 ). The TPB assumes that volitional human behaviour is a function of (1) one’s intention to perform a given behaviour and (2) one’s perception of behavioural control (PBC) regarding that behaviour ( Figure 3 ). Furhermore, intentions are influened by one’s attitudes towards the behaviour (e.g. cognitive attitudes : is the behaviour good or bad?; affective attitudes : is the behaviour pleasant or unpleasant?), one’s subjective norm beliefs (e.g. descriptive norms : do others perform the behaviour?; injunctive norms : do others who are important to me want me to perform the behaviour?), and one’s perceptions of control regarding the behaviour (e.g. self efficacy : level of confidence to perform the behaviour; perceived control : barriers to stop the behavoiur being performed). The extent to which PBC influences behaviour directly, rather than indirectly through intention, depends on the degree of actual control over performing the behaviour (Sniehotta, Presseau, & Araújo-Soares, 2014 ). The TPB has been a dominant theoretical approach in health behaviour research for a number of decades and has been examined extensively. The vast majority of studies have used correlational designs to investigate cross-sectional and prospective associations between TPB variables and behaviour (Noar & Zimmerman, 2005 ); systematic reviews indicate that the TPB accounts for approximately 20% of variannce in health behaviour, and that intention is the strongest predictor of behaviour (McEachan, Conner, Taylor, & Lawton, 2011 ).

Theory of planned behaviour.

Following receipt of ethical approval from the local university REC (2014/6/15), students completed a questionnaire regarding regular exercise (Datafile in supplementary material). This cross-sectional dataset is used here to illustrate how to conduct a network analysis and comprises the responses of 200 students to a TPB questionnaire, which included the following items relating to regular exercise (i.e. exercising for at least 20 min, three times per week) for the next two months:

Att1 : belief that engaging in regular exercise is healthy

Att2: belief that engaging in regular exercise is useful

Att3 : belief that engaging in regular exercise is enjoyable

Dnorm1 : descriptive norms for friends regarding engaging in regular exercise

Dnorm2 : descriptive norms for other students regarding engaging in regular exercise

Injnorm1 : injunctive norms for friends regarding engaging in regular exercise

Injnorm2 : injunctive norms for students regarding engaging in regular exercise

Pbc1 : perceived control regarding engaging in regular exercise

Pbc2 : self-efficacy towards engaging in regular exercise

Intention : intention to engage in regular exercise

In the Environment/History/Connection pane, we can select Import Dataset to import the datafile. Alternatively you can use the command code:

TPB2018 = read.csv("filename.extension", header = TRUE).

The filename extension is simply the location of the relevant csv. file on your computer.

Once it is imported, the data will appear in the Editor pane and the console window will have a line of code indicating that data is active

>View(TPB2018)

The next step is to tell R to estimate the network model using the EBICglasso to produce an interpretable network. The command line below tells R to label the results as ‘Network.’

Network <- estimateNetwork(TPB2018, default = "EBICglasso")

Once we have estimated the network, we can ask R to plot it.

>plot(Network, layout = "spring", labels = colnames(TPB2018))

These commands will produce the network plot with the variable names in the plot ( Figure 4 ).

Network analysis of TPB items. The size and density of the edges between the nodes respresent the strength of connectedness.

The network shows the strength of relationships between the TPB variables. Some variables have quite strong connections (e.g. att2 and att3 ; injnorm1 and dnorm1 ), whereas others have weak relationship (e.g. att1 and pbc1 ). Visual inspection of the network reveals that the network seems to split into three different communities: (1) the normative beliefs cluster together; (2) the three attitudinal variables and the pbc1 item seem to cluster, and (3) the pbc2 and intention item cluster together. However, visual inspection of the graphical display of complex relationships requires careful interpretation, especially if there are a large number of nodes in the network. In order to check the presence of the potential 3 communities, a spinglass algorithm was applied to the network using the igraph R -package. Of note, this analysis supported the 3 community interpretation (Interested readers are referred to Eiko Fried’s tutorial on this topic: http://psych-networks.com/r-tutorial-identify-communities-items-networks/ ).

Next we can examine the centrality indices in terms of Betweenness, Closeness and Strength ( Figure 5 ).

Centrality indices.

>centralityPlot(Network)

Att 3 had the highest strength value and a high closeness value: it has strong connections to the nodes nearby. It plays an important role in the network and its activation has the strongest influence the other nodes in the network. However, pbc1 and injnorm1 had the highest betweenness values: they act as the bridge connecting the communities of nodes.

Stability of the centrality indices

As noted previously, the stability of centrality indices can be examined by estimating network models based on subsets of the data. The case-dropping bootstrap ( type = "case" ) is used; in this case 1000 bootstrapped samples were estimated.

>CentralStability <- bootnet(Network, nBoots = 1000, type = "case")

The CS coefficients for each index can be produced:

>corStability(CentralStability)

A table presenting summary data (e.g. M , SD, CI s) on the bootstrapped indices can be created.

>summary(CentralStability)

However, it may be more useful to plot the stability of centrality indices:

>Plot(CentralStability)

Figure 6 shows the resulting plot of the centrality indices. As the percentage of the sample included in the estimates decreases (as illustrated on the X-axis, the subset samples decrease from 95% of the original sample to 25% of the sample), there is a drop in the correlation between the subsample estimate and the estimate from the original entire sample. Once the correlation goes below .7, then the estimates become unstable. For example, using 90% of the original sample, there is steep decrease in accuracy of the betweenness estimate, whilst the stability of the strength and closeness estimates declines at a slower rate. However, with a subset sample of 70% of the original participants, the closeness estimate is now correlating less than .7 with the full sample estimate. When the subset sample comprises 50% of the original sample, the strength estimate falls below .7. Overall, the pattern suggests the stability of the centrality indices for closeness and betweenness are not that reliable: of note, strength tends to be the most precisely estimated centrality index in psychology networks, and betweenness and closeness only reach the threshold for reliable estimation in large samples (Santos, Kossakowski, Schwartz, Beeber, & Fried, 2018 ).

Stability of central indices.

Edge weight accuracy

The robustness of the edge weights can be examined using bootstrapped confidence intervals.

> EdgeWgt<- bootnet(Network, nBoots = 2500)

Similar to the centrality indices, a summary table of the results of edge accuracy analysis can be produced (e.g. M , SD, CI s for estimates):

summary(EdgeWgt)

The plot of the bootstrapped CIs for estimated edge parameters provides a visually informative representation of the estimates.

> plot(EdgeWgt, labels = TRUE, order = "sample")

Figure 7 has been modified to remove most of the names of the edges being represented on the Y axis to de-clutter the figure to enhance readability. The red line in Figure 6 shows the edge value estimated in the sample, and the grey bars surrounding the red line indicate the width of the bootstrapped CIs. Of note, many of edges are estimated as zero (e.g. dnorm2 - att3 ). Some edges are larger then zero, but the bootstrapped CIs contain zero (e.g. att3 - intention ), and for a smaller number of edges, the estimates are larger than 0 and the CIs do not including zero (e.g. dnorm1 - injnorm1 ). Given the above pattern of CIs for the edge weights, the network should be interpreted with caution.

Accuracy of the edge-weight estimates (red line) and the 95% confidence intervals (grey bars) for the estimates.

The data were used to illustrate how to run network analysis. Typically such data are analysed by combing the items into their higher order construct (e.g. Attitudes, Norms, PBC, and Intentions) and then multiple regression examines the extent to which variation in Attitudes, Norms and PBC accounts for variation in Intentions, and which variables have significant relationships with intentions (Noar & Zimmerman, 2005 ). Network analysis allows us to examine how the items relate to each other and can reveal important structural relationships that regression cannot reveal. If the present network was replicated and using larger samples, then we could interpret the network in terms of its structural implications for the TPB.

Contrary to the theory, not all variables were directly related to intentions; for example att2’s (belief that exercise is useful) relationship to intention was mediated by its relationship to att1, att3 and pbc1. Indeed, all of the subjective norm items were related to intentions through a mediated pathway with pbc1. Although in line with the TPB, the normative beliefs are related to each other and form a community (i.e. the normative variables correlate with each other), in the current network, contrary to the theory, these normative beliefs have no direct relationship with intentions and only a weak relationship to PBC. This finding would indicate that your intentions to exercise are not that influenced by either the exercise behaviours of others or what you believe others would like you do in terms of regular exercise. Rather, the network suggests that your beliefs about other’s exercise only influences your perceptions of control over exercise, e.g. if others are exercising and want you to exercise, you may feel that you have more control over whether you exercise (‘if others can do it, then so can I’), and by feeling in control, you may have higher intentions to then exercise. A previous meta-analysis similarly reported lower correlations between subjective norms and intentions for physical activity behaviour compared to the strength of relationships between attitudes and intentions, and between PBC and intention (Hagger, Chatzisarantis, & Biddle, 2002 ).

Among the attitudinal variables, the affective attitude is the central node as it connects not only to all the other attitude variables but also to both PBC items (in line with theory) and the Intention item. Research has highlighted the role of affective attitudes on behaviour (e.g. Lawton, Conner, & McEachan, 2009 ) and the present data highlight the value in conceptualising normative beliefs as comprising affective/experiential and cognitive/instrumental components (Conner, 2015 ).

The model also found that the self-efficacy variable (pbc1) of PBC had the highest closeness to intentions; the strong relationship between self-efficacy and activity intentions is consistent with previous meta-analyses (Hagger et al., 2002 ). The fact that the two PBC items had differing patterns of relationships with the other TPB variables further supports the proposed distinction between the self-efficacy and perceived control components of PBC (Conner, 2015 ). If replicated using within person networks, the findings may suggest that changes self efficacy might directly impact on intentions and changes in affective attitude might impact on the other attitudinal variables, and given the network model, a change in Att1 provides a route to influence Pbc2, which should further strengthen the intentions. In essence the network reveals that for regular exercise behaviour among the student population, the affective attitudinal variable is the strongest node and therefore interventions could prioritise targeting changing the emotional responses to exercise to increase intentions to exercise. The network gives little support to intervening to change normative beliefs. This section indicates how network analysis in principle can influence not just how we appraise the pathways proposed in our theories, but also how it may offer guidance for interventions.

The present example aimed to highlight some of the key aspects to conducting network analysis in R and how to make sense of the outputs. Many real world networks estimated in psychology are likely to be messy and therefore interpretations require tempering in light of the stability and accuracy of the estimates. As network analysis becomes more prevalent, replication of network structures and properties will give greater confidence in the interpretations of the network patterns.

Of note, the psychosystems group has also developed an online web app ( https://jolandakos.shinyapps.io/NetworkApp/ ) that allows researchers to visualise and analyze networks from data uploaded into the app. The app, based on the R packages describe above, can analyse data in different common formats (e.g. ‘.csv’, ‘.xls’ and ‘.sav’) and the data can represent the raw data, the correlation matrix between the variables, an adjacency matrix, or an edge list. The user can inform the app how missing data were coded and can also apply the non-paranormal transformation for data that are not normally distributed. The app provides the various options outlined in this paper for estimating the network structure from the raw data; these include the GLASSO, the graphical VAR, and multilevel VAR. The network default is to use the Fruchterman-Reingold Algorithm to layout the network and the user can decide various visual settings (e.g. size of nodes). It also calculates the centrality (strength, closeness and betweenness) indices to determine a node’s importance in the network. A clustering analysis can be run on the data and the networks from two groups can be compared. This resource offers a very user-friendly means to start to examine network structures in data.

Barabási ( 2012 ) argued that theories cannot ignore the network effects caused by interconnectedness among variables. Health psychological processes reflect complex systems and to understand such systems, we need to understand the networks that define the interactions between the constituent variables. Many of our core health psychology models comprise networks of interacting constructs. Considering such psychological processes and outcomes from this perspective offers alternate ways of conceptualising and answering important psychological questions. Networks evolve over time due to dynamical processes that add or remove nodes (variables) or change edges (relationships between variables): the power of network science derives from the ability of the network to model systems where the nature of the nodes (e.g. symptoms, behaviours, beliefs, physiological arousal) and the edges (e.g. correlational relationship, causal relationship, social connection) can vary. Network analysis as a technique has been briefly outlined and how to conduct a simple analysis in R was presented. Hopefully this brief paper will encourage health psychologists to think about their data in terms of networks and to start to apply network analysis methods to their research questions. The work of Borsboom and colleagues provides a key foundation for network analyses and, as mentioned at the start of this paper, their invaluable contributions to the applications of network theory to psychology cannot be underestimated. Understanding the dynamic patterns of networks may offer unique insights into core psychological processes that impact health and well-being.

1 We wish to thank an anonymous reviewer for highlighting this possibility.

Disclosure statement

No potential conflict of interest was reported by the author.

David Hevey http://orcid.org/0000-0003-2844-0449

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Network analysis: emergence, criticism and recent trends

RAUSP Management Journal

ISSN : 2531-0488

Article publication date: 22 November 2019

Issue publication date: 9 December 2019

Network analysis is a well consolidated research area in several disciplines. Within management and organizational studies, network scholars consolidated a set of research practices that allowed ease of data collection, high inter case comparability, establishment of nomological laws and commitment to social capital motivation. This paper aims to elicit the criticism it has received and highlight the unsettled lacunae.

Design/methodology/approach

This paper sheds light on Network Analysis’s breakthroughs, while showing how its scholars innovated by responding to critics, and identifying outstanding debates.

The paper identifies and discusses three streams of criticism that are still outstanding: the role of human agency, the meaning of social ties and the treatment of temporality.

Originality/value

This paper brings to fore current debates within the Network Analysis community, highlighting areas where future studies might contribute.

• Social capital
• Network analysis
• Economic sociology
• Relational sociology

Kirschbaum, C. (2019), "Network analysis: emergence, criticism and recent trends", RAUSP Management Journal , Vol. 54 No. 4, pp. 533-547. https://doi.org/10.1108/RAUSP-05-2019-0074

Emerald Publishing Limited

Copyright © 2019, Charles Kirschbaum.

Published in RAUSP Management Journal . Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode

Introduction

Throughout all social sciences, the imagery of “networks” has sparked the imagination of scholars and practitioners ( Castells , 2000, 2016 ; Knox, Savage, & Harvey, 2006 ). Network Analysis research has gained in the last decades a position of centrality in Management studies ( Borgatti & Halgin, 2011 ). Within the last decade, Network Analysis scholars have consolidated this approach’s core premises, while addressing enduring criticism. In contrast to a view that Network Analysis is mainly macro, scholars have shed light on studies that emphasize individual choice and individual personality ( Fang et al. , 2015 ; Tasselli, Kilduff, & Menges, 2015 ). Instead of a conception of networks as static and bearing deterministic effect on individual performance, several reviews have unearthed research efforts that highlight change and dynamics ( Borgatti, Brass, & Halgin, 2014 ; Tasselli et al. , 2015 ). In contrast to a perception that Network Analysis is fully committed to a structural perspective, recent manuscripts attempted to underscore human agency ( Borgatti et al. , 2014 ; Gulati & Srivastava, 2014 ; Kilduff & Brass, 2010 ). In opposition to views that conceive the patterns of relations as dissociated to culture and meaning, several recent studies have brought back a concern with meaning ( Borgatti et al. , 2014 ). These studies have expanded Network Analysis’s boundaries and theoretical interfaces.

In spite of this expansion, studies following the Network Analysis approach have reinforced its association to social capital and the idea that social ties bring positive gains ( Carpenter, Li, & Jiang, 2012 ; Hollenbeck & Jamieson, 2015 ; Kilduff, Tsai, & Hanke, 2006 ; Kilduff & Brass, 2010 ). Consequently, Network Analysis have continuously inquired how individual prominence is associated with performance ( Kilduff & Brass, 2010 ). In tandem, Network Analysis has strengthened its concern with operationalizing network centrality measures as a key approach to identify influential individuals ( Kilduff et al. , 2006 ). Therefore, it has deemphasized studies that focus on the social system, towards research efforts that emphasize individual agency. Throughout this article, I claim that while several studies have successfully incorporated “human agency”, improved the discussion around the meaning of relationships and incorporated the treatment of temporality, these themes still fall short from a with engagement with Network Analysis critics ( Emirbayer & Goodwin, 1994 ; Erikson, 2013 ). This paper builds upon the existing criticism to Network Analysis and contributes to this debate as it goes deeper on the “human agency”, “temporality” and “meaning themes”.

The purpose of this paper is threefold. First, it brings evidence of the emergence and prominence of the Social Capital approach over other alternative approaches within the Network Analysis in management studies. Second, it portrays the historical evolution of Network Analysis, with emphasis on the major empirical and methodological breakthroughs that led to the emphasis on Social Capital. Third, recover the major criticism against the Network Analysis mainstream, while highlighting how the Network Analysis mainstream’s responses addressed this criticism. Finally, the paper concludes with possible avenues of future developments for Network Analysis, while identifying the major obstacles for a full dialogue with alternative approaches.

To contextualize the Network Analysis within the management studies scholarship, I chose to identify the articles that were ever published at flagship journals that cite specific core concepts. The journals chosen were ASQ, AMJ, AMR, Org Science, Org Studies, JMS, and SMJ. To represent the evolution of the volume of papers associated to “social capital”, I chose the “betweenness” and “structural hole” terms, as they are widespread metrics of individual success within networks. In contrast, I chose the term “blockmodel” to identify the papers associated with a system approach to Network Analysis. These terms and approaches will be further elaborated in the coming sections in this paper. An examination of the evolution of a number of articles that cite these terms at the selected journals shows that this research stream has carved out an important segment ( Figure 1 ).

This picture enacts a scholarly community heralded by a successful research project. Yet, the history of Network Analysis research entails an intense debate, conflict and displacement. Consider for instance the evolution in the citation patterns of the three concepts cited above (betweenness, structural hole, and blockmodel) in Figure 2 . While “blockmodel” comprised the majority of citations in the late eighties, early nineties, it vanished to almost oblivion by 2010. This fall is not just explained solely by an expected “obsolesce” of concepts. It also reveals major shifts in the field. The “blockmodel” approach was mainly used to understand a network as a system of social roles, it favored unique case studies, rich in contextual grounding, and combination of several types of relationships at once. In contrast, “betweenness” and “structural hole” are concepts associated with individuals’ brokerage capacity, where the whole network or the social context is frequently elided to the background, thereby maximizing the generalizability of findings.

This example illustrates the need of exploring how SNA evolved through time, unearthing its central debates ( Borgatti & Halgin, 2011 ; Emirbayer & Goodwin, 1994 ; Kilduff et al. , 2006 ; Pachucki & Breiger, 2018 ). This article follows this extant literature by exploring how the SNA tradition evolved and developed its “hardcore”. Further, it inquiries how its defenders answer to critics, and as a consequence, introduce novelties to the discipline.

Early network analysis research program: foundational ideas

The Network Approach, like any other discipline, lays on widely accepted beliefs ( Freeman, 2004 ; Kilduff et al. , 2006 ). At this paper, I suggest that two beliefs are widely shared by several streams of Network Analysis: the primacy of relations and the structural patterning of social life.

Network Analysis is based on “the primacy of relations”, which implies a strong ontological program. In comparison to “essentialist” approaches that assume individuals as “self-contained” entities, relational programs and Network Analysis specifically attempt to understand the individual as emergent of its web of relations. Further, Network Analysis places its analyses on sets of individuals linked by edges, which are amenable to the mathematical graph theory analysis ( Freeman, 2004 ). As a result, it shies away from purely “individual variable-centric” models ( McFarland, Diehl, & Rawlings, 2011 ).

Network Analysis scholars attempt to unveil the “structural patterning of social life” through mathematical models. These models might comprise the identification of prominent individuals in a network, of whole networks’ characteristics, and the identification of emergent groups and positions in the network, or the underlying mechanisms in tie formation ( Freeman, 1979 ; Kilduff et al. , 2006 ; Snijders, 2011 ; Wasserman & Faust, 1997 ). Even when the focus is a qualitative study, SNA research will bring graph-based representations to the fore ( Domínguez & Hollstein, 2014 ).

The early network analysis research tradition: emphasis on meaning, context and social systems

In 2004, Linton Freeman wrote a book called “The Development of Social Network Analysis”, where he attempted to reconstruct the genealogies across the Network Analysis community ( Freeman, 2004 ). His identification of Network Analysis’s forefathers included Simmel, Moreno, Heider and Lewin as great influences. Before World War II, several initiatives were undertaken at both sides of the Atlantic. This effort included scholars like George Caspar Homans, William Foote Whyte and Elton Mayo. The late thirties “Western Electric Company” studies, a precursor of the Human Relations school in management mapped six types of relations among employees and espoused preliminary social network depictions (sociograms) ( Roethlisberger, Dickson, Wright, & Western Electric Company, 1967 ). Yet, it was at the late fifties and early sixties that the Network Analysis research blossomed, mainly as a response to the “structural functionalist” hegemony. It is worth concentrating on two specific hubs: Harvard University and Manchester communities.

Led by Max Gluckman during the fifties, the social Network Analysis approach at Manchester clashed directly against the structural functionalism’s theory and methods ( Mitchell, 1969 ). While the structural functionalism conceived social relations as overdetermined by legitimate social norms, Manchester school anthropologists identified and documented empirical evidence of social relations that did not align with the expected rules. Drawing from kinship studies, these scholars showed that the institutionalized rules governing relationships could conflict with each other. The conflict among rules gave individuals to the opportunity of increasing their discretion in forming relationships ( Nadel, 1957 ). Consequently, scholars committed to Network Analysis placed social relations in a privileged starting point: social relations could not be reduced to social norms and institutions ( Emirbayer, 1997 ). The Manchester’s approach to Network Analysis generated a body of studies that were highly contextualized. The study of relationships was always conducted in tandem with ethnographic fieldwork. Further, field research captured several different types of relationships, collected through interviews as well as direct observation. Scholars associated with the Manchester school also combined interdisciplinary approaches to their field methods, to obtain a wholistic perspective on interviewees. Substantively, these studies were ambivalent vis-à-vis the effect of social relations on individuals’ outcomes. As several studies attempted to show, one’s entrapment into clientelist relations could be harmful.

In the late sixties and seventies, scholars located at the Harvard University developed a set of tools and approaches that paralleled Manchester’s. Freeman (2004) calls this period the “Renaissance” of Social Network Analysis at Harvard and crucial for the further development of the discipline. The major propelling force for this emergence was the hiring of Harrison White, a scholar with training in both Physics and Social Science. The efforts of Harrison White and his colleagues were concentrated into using the concept of “structural equivalence” and develop it into the idea of “network positions”. “Structural Equivalence” refers to the extent that individuals’ patterns of relations are alike. For that matter, structurally similar individuals would be equally connected to alters in a network. White and his colleagues went a step further and suggested that sets of individuals that were structurally similar should be grouped together into “positions” (the “blockmodeling” approach). Further, the relationships between positions (“blocks”) could be also analyzed. As a consequence, complex and large networks could be summarized into a collection of interlocked positions ( White, Boorman, & Breiger, 1976 ).

White et al. (1976) show that these “positions” are conceptually equivalent to “social roles”, since individuals who share the same pattern of relations are probably facing the same social pressures. Yet, in comparison to the functional structuralist approach to social roles, White and associates’ approach let roles emerge from the patterns of social relations, rather than biasing the study with ex-ante rule-based relationships. White’s insights led to several strides within the organizational theory and the sociology of organizations. For instance, DiMaggio (1986) proposed that “organizational fields” analysis could be complemented with blockmodeling of the field’s actors. Bearman (1987) analyzed the English revolution between 1540 and 1640 and suggested that the emergence of network positions preceded the emergence of ideologically cohesive discourses. In a similar vein, Padgett & Ansell (1993) reconstructed the networks among Florentine families (comprising several types of relations) and showed that occupying a network position preceded one’s enactment of social identity. These later studies suggested that the individual’s actorhood was best conceptualized as an outcome, not antecedent to social relations. Hence, this research stream frequently espoused a “network reductionism”, where relations were prior to individuals’ interests and identities ( Emirbayer & Goodwin, 1994 ). More balanced approaches attempted to establish individuals and network membership in a dual constitutive relation ( Breiger & Melamed, 2014 ; Kilduff & Krackhardt, 1994 ).

The emergence of social network analysis social capital approach

In the late seventies, but mostly during the eighties and nineties, Network Analysis would suffer a shift that established the construction of its current mainstream core, mainly due to Mark Granovetter and Ronald Burt translations of the idea of “social capital” into network constructs. At this paper, I espouse a restricted definition of social capital, offered by Adler and Kwon:

Social capital is the goodwill available to individuals or groups. Its source lies in the structure and content of the actor's social relations. Its effects flow from the information, influence, and solidarity it makes available to the actor. ( Adler & Kwon, 2002 , p. 2002).

From this perspective, individuals access important resources through their relationships, thus there is an emphasis on individual and instrumental action. Further, resources and relations are conceived as analytically if not empirically separated. The effort of bringing the idea of social capital to Network Analysis had already been developed by James Coleman and Nan Lin ( sociologists strongly influenced by their economist peers at the University of Chicago; see Coleman, 1990 ; Lin, 2001 ). Both Granovetter and Burt were influenced by Coleman and Lin and revolutionized Network Analysis and the Economic Sociology. They did that by recovering the taxonomy of triads, developed by social psychologists but seldomly used by sociologists.

Inspired by Fritz Heider (1958) , several social psychologists were interested in understanding whether individuals would be able to cope with perceived dissonance within their social contacts ( Cartwright & Harary, 1956 ; Festinger, 1957 ). These initial investigations led to the insight that individuals would not suffer from “cognitive dissonance” if their perceived surrounding contacts were organized into transitive triads. For instance, if Mario is friends of Rafael, and Rafael is friends of Sandro, we would expect that Mario would be willing to be Sandro’s friend. Conversely, those triads that were intransitive were labeled “forbidden triads”. This research stream later received further mathematical treatment into a probabilistic model of a finite set of triads ( Holland & Leinhardt, 1970 ).

Under the supervision of Harrison White, Granovetter recovered this taxonomy of triads and suggested that “weak ties” could endure and emerge as bridges in a social system, provided that they were not surrounded by strong ties ( Granovetter, 1973 ). By “tie strength”, Granovetter understood the emotional investment but also the resources spent in the relationship. When two individuals (say, MaryJo and Luciana) are close to a third-party (Fabio), Granovetter suggested that MaryJo and Luciana should have at least a weak tie between them. This insight could be unfolded into three implications: first, Granovetter preserved the idea of “forbidden triad”, for triads with two strong ties could be at least complemented with a weak tie; second, it offered an important complement to Coleman idea that “social capital” was based on strong and cohesive networks. Instead, to obtain fresh information, one should be able to access opportunities outside her own community, through bridges to other parts of the system (weak ties). Third, Granovetter also introduced an important methodological novelty: while a tie’s strength was defined vis-à-vis the emotional proximity between ego and alter, it could be operationalized as a sheer share of time that ego spent with alter, simplifying the data collection.

Ronald Burt, a student of Coleman and Lin at Chicago, had also leveraged on the insight of triads and developed upon Granovetter’s ideas. Further, Burt also brought to Network Analysis several anchors that helped it to reduce complexity allowing intercase comparability, generate universal laws, and center the analysis on individual action. In the early eighties, Burt was involved in the analysis of a census conducted in the state of California, where the individual relational data was collected. The questionnaire captured a wide range of types of social ties. Burt’s analysis of individuals’ social ties vis-à-vis life attainment (a core principle at the social capital tradition) revealed that “trust” relations were sufficient to capture most variation in explaining individual achievement ( Burt, 1984 ). This finding allowed future studies to forego the examination of multiple types of relations, simplifying both the collection and data analysis, while permitting enhanced comparability between cases.

In contrast to James Coleman, who emphasized cohesion in one’s network as a source of social capital, Burt emphasized disconnection between contacts. For Burt, borrowing on Simmel, when one’s network encompassed many contacts, and these contacts were disconnected from each other, this allowed the individual to amass a greater wealth of information and eventually promote a broker role among those disconnected contacts ( Burt, 1992 ). Thus, Burt emphasized the “forbidden triads”, trespassing a boundary Granovetter avoided to cross. In a sequence of studies, Burt was able to replicate this insight in a number of different contexts, attempting to promote the “structural hole” advantage into a nomological law, and at the same time, displacing his teachers’ previous insights on social cohesion to the background ( Burt , 2001, 2004 ).

Following Lin’s approach, Burt also focused on “ego networks”, rather than “whole networks”, allowing the analysis of single respondents to standardized questionnaires. This shift encompassed two moves in relation to the previous paradigm. First, while the previous paradigm was usually based on the whole network data collection, the later paradigm was mainly focused on data based on individuals’ direct contacts only (ego network). That allowed researchers to waive the collection of “whole network” relational data. In contrast, it would be possible to collect data from individuals, assuming independence of observations. Second, while the previous paradigm characterized one’s centrality in the network as emergent of all paths in a network, the later paradigm was only concerned on how one’s direct contacts were related to each other. Burt’s strategy to debunk the previous beliefs entailed an empirical comparison between “whole-network based” social capital and “ego-network based” social capital. He concluded that “contacts of contacts” are irrelevant for one’s social advantage, allowing future studies to detach individuals from whole relational systems ( Burt, 2007 ).

The social capital turn in Network Analysis scholarship triggered a fast diffusion of this technique into the management community for several reasons: first, it allowed the generation of universal (nomological) laws, easily transposable to new contexts; second, it focused on the positive side of “networking”, where connections were usually assumed to be associated to economic gains ( Kilduff et al. , 2006 ); third, it brought quick and fast data collection methods based on questionnaires, easily adaptable. In sum, these changes allowed the possibility of translating these insights to management teaching: how to recognize and leverage on their structural social capital advantage ( Burt & Ronchi, 2007 ). Table I summarizes the shift that “social capital” scholars introduced to SNA studies.

Criticism to social capital mainstream and responses

In parallel to the emergence and consolidation of the “social capital” paradigm, criticism was offered, internally and outside the Social Network community. In this section, I will present three major themes that were presented as criticism to Network Analysis, as well as the responses developed by Network Analysis mainstream.

Structural determinism and structuralist instrumentalism

One of the most important sources of criticism to Network Analysis approach is its “structural determinism” ( Emirbayer & Goodwin, 1994 ). Critics pointed out that studies usually emphasized only the structural effects on individuals, eliding how individuals attained their advantageous positions by establishing and disrupting ties. This line of criticism remained strong for several decades ( Borgatti & Halgin, 2011 ).

This criticism was frequently collapsed into the remark that network studies lacked a theory of change, for longitudinal analyses could try to explore how social actors established and disrupted ties. To be sure, these two criticisms should not be confused. A theory of change might be restricted to show how individual action (micro) aggregates into network evolution (micro-macro link). Yet, the individual predisposition for action might be overdetermined by her network position. What Emirbayer and Goodwin (1994) referred as “Structural instrumentalism” is the favorite approach adopted by proponents of longitudinal networks, as I will explore further above ( Snijders, 2011 ).

In contrast to the “structural determinism” and “structural instrumentalism” approaches, Emirbayer and Goodwin (1994) suggest the adoption of the “structuralist constructionism”. This approach takes in full account the individual’s possibility of exercising agency, and conceives actors as dialogical, while avoiding assuming individuals as “self-sufficient entities” ( Emirbayer & Mische, 1998 ). Emirbayer and Mische (1998) define human agency as:

[…] the temporally constructed engagement by actors of different structural environments – the temporal relational contexts of action-which, through the interplay of habit, imagination, and judgment, both reproduces and transforms those structures in interactive response to the problems posed by changing historical situation. (p. 970)

In contrast to the “structural determinism”, under this approach individuals exert choice (although under constraints). In contrast with the “structural instrumentalism”, individuals are not conceived as maximizing utility out of fixed maximization rules. Interpretative understanding of concrete situations might lead actors to reframe situations and rechannel their efforts ( Gross, 2009 ; Padgett & Ansell, 1993 ).

Introducing agency to mainstream network analysis.

Current attempts to reintroduce human agency into Network Analysis have usually conflated agency to individual action. At this section, I present how psychologists, rational action sociologists, and economists have conceived agency within networks.

Psychologists associated with the current Network Analysis scholarship have usually attempted to correct the overtly structuralism by reintroducing individual attributes into the analyses ( Kilduff & Krackhardt, 1994 ). One approach was to introduce individuals’ personality attributes into the models, to explore how personality traits explain tie formation and position attainment ( Mehra, Kilduff, & Brass, 2001 ). A similar strategy was to explore the individuals’ social cognition skills, and attempt to establish the extent that one’s position in the network is explained by her cognitive skills ( Kilduff & Tsai, 2003 ; Krackhardt, 1987 ). While these approaches have helped to improve the “micro-macro” linkages in the Network Analysis research, they have scarcely helped to explain why individuals make their choices, thus eliding the agentic dimension of social action.

Another Network Analysis mainstream family of responses to the lack of agency in Network Analysis studies has been largely associated to an attempt of modeling longitudinal behavior, thus, conflating “agency” to “change” (reinforcing the ‘Structuralist instrumentalism' approach). For instance, the SIENA project has proposed an actor-based simulation that attempts to infer what social actors value in a social network when they form and disrupt ties. This approach is based on approximating the observed network waves to the simulated networks, assuming that actors want to maximize utility ( Snijders, 2011 ).

Agency has been introduced to Network Analysis by scholars following alternative streams, but often with a “utility maximization” approach ( Gulati & Srivastava, 2014 ). For instance, computational social scientists attempt to create ex-nihilo networks solely based on simulations. A remarkable example of a contribution based on computational simulation is Buskens & Van de Rijt's (2008) model of a network as if everyone strove to control structural holes. Their simulations show that if all individuals in a network strove for structural holes, their relative gains would be completely depleted.

Economists have also attempted to give a contribution to the problem of agency in SNA ( Jackson, 2008 ). Economists usually espouse Nash equilibrium modeling, frequently combined with experiments that might confirm the equilibria deduced by theory. For instance, Galeotti & Goyal (2010) show that under circumstances of minimum asymmetries of expertise among individuals, participants of a network will organize themselves around a “star-shape” (centralized) network. Finally, physicists have developed sophisticated modeling and simulation approaches to explain the emergence of complex structures ( Barabási, 2003 ).

Meaning of ties and forms

Critics of Network Analysis have pointed out that this scholarly community used to take as granted a dichotomy between “form” and “content” of ties ( Emirbayer & Goodwin, 1994 ). As a result, relations appear to be “tubes” throughout which “stuff” (values, norms, beliefs, information about jobs opportunities, ideas) flow. As we have seen before, the analytical separation between structure and culture (or, the pattern of ties and the meanings that circulate) was a central assumption for social capital proponents.

Erikson (2013) traces back this approach to Simmel’s early studies, whose sociological project entailed bringing to sociology an analogue of Kantian pre-experience categories of “time” and “space”. For Simmel, argues Erikson, the shape of relationships (e.g. transitive triads) is prior to experience. Thus, these universal shapes work as pre-content cognitive schemata that shape the individual perception of situations. For instance, Simmel compares two men wooing a woman to two firms competing for the same customer as similarly conducing to conflict, regardless of the content that is expressed throughout these interactions.

Scholars have deployed several strategies to challenge this dichotomy. One strategy is to show that ties are endogenous to what flows throughout them. In other words: what goes through a relationship changes it. For instance, Zelizer (2005) shows that the exchange of money between two persons might change their relationship. For instance, if a girlfriend gives money to her boyfriend after sex, this could offend the later and ruin the relationship.

Several critics have pointed that ties should not be taken as “things” that an actor possesses and is able to act upon this. In contrast, McLean (1998 , 2007 ) shows how social actors deploy rhetorical resources to attempt framing how interactants and third parties will interpret the content of a relationship. In opposition to the dichotomy between “form” and “content”, several critics suggest that ties are constituted by meaning, and without a prior framework of reference, social actors are unable to recognize a relationship with alters ( White, 2008 ).

(Re) introducing “meaning” to the mainstream.

Network Analysis has slowly encompassed multiple types of relations. For instance, Ibarra’s (1992) distinction between “instrumental” and “expressive” ties has been a dominant approach to differentiate ties within Network Analysis scholarship. Recent reviews have acknowledged the paucity of types of relations applied in Network Analysis ( Borgatti et al. , 2014 ). One recent answer to this criticism is the return to ethnography as a starting point for any research project ( Borgatti, Everett, & Johnson, 2013 ). Borgatti and his associates suggest that any research design should include an “ethnographic sandwich”, where the identification of the most important types of relations is conducted before the relational data collection.

Further, several new approaches have been developed to extend the simultaneous analysis of several types of relations. The analysis of “multiplex” (several types of relations) networks has gained traction in the last years, exploring the groups of actors more likely to develop reciprocity and other configurations based on different types of relations ( Agneessens & Skvoretz, 2011 ). The same idea is extended to strategic management and organizational studies, by studying strategic alliances and merger and acquisition ties ( Shipilov, 2012 ; Shipilov & Li, 2009 ).

Further, recent studies have attempted to reincorporate negative ties. Negative (or conflictive) ties were mostly emphasized by Heider’s balance theory, and lost room, as the social capital and the positive organizational relations approaches led to an emphasis on positive relations ( Kilduff et al. , 2006 ). In contrast, recent scholarship has stressed the role of negative ties to individual outcomes ( Labianca, 2014 ). These studies are complementary to the social capital approach, as they attempt to clarify how negative relations undermine social capital predictions.

Temporality

The attempts of modeling network change with sophisticated longitudinal models have spurred the debate on how temporality is conceived within Network Analysis studies. Critics have pointed at least three problems associated with Network Analysis mainstream treatment of time.

First, the models assume that individuals experience time as a homogeneous and linear flow ( Abbott, 2001 ). While at some circumstances and contexts events occur at a faster pace, in other situations, events are experienced as fewer and longer.

A related problem is what Granovetter dubbed “presentism” in SNA ( Granovetter, 1992 ). The “presentism” is the assumption that social actors think their relations in an ahistorical fashion as if they don’t have a history, and there are no expectations on their future existence. This problem became more salient as critics to questionnaire as reliable devices for relational data collection came to scrutiny. It became apparent that respondents confused “existing relationships” with relationships that they wanted to preserve in the future ( Martin, 2017 ).

Finally, critics have pointed out that users of longitudinal models were frequently forced to create a collection of “snapshots” before modeling network change. As a result, intermediary data has been lost in the process. Moreover, by flattening relational data into a single point in time, the resulting structures might be misleading ( Butts, 2009 ). As Big Data is incorporated into the toolbox of social scientists, the temporal resolution problem becomes even more acute, requiring better models that are appropriate to frequent changes in small temporal units ( Pachucki & Breiger, 2018 ).

Introducing more developed approaches to temporality.

A major recent breakthrough in the Network Analysis mainstream was to establish a clearer distinction between “relational events” and “relational states” and its implications for research ( Borgatti et al. , 2013 ). “Relational events” are observable interactions, recorded by the interactants themselves or third-party observers. For instance, a hand-shake is a relational event. In contrast, “relational states” are usually perceptions of a relationship between individuals or enacted by third parties. For instance, when two individuals get married, they are objectively bound in a relationship state. Further, when one recognizes a classroom peer as a “friend”, this is also a disclosure of “relational state”, although subjective.

This distinction led Network Analysis scholars to develop the models through two different directions. One possibility is the modeling of relational states as the outcome of relational events. For instance, Gibson (2005) applies Conversational Analysis to infer relational states from interactions (relational events) occurred in a series of meetings. Another possibility has been to model the dynamics of “relational events”, circumventing the arbitrary establishment relational states. For instance, the “Relational Event Modeling” approach ( Butts, 2008 ) infers the relational mechanisms from a stream of interactions ( Quintane, Conaldi, Tonellato, & Lomi, 2014 for an example in the organizational literature).

Discussion and conclusion

Throughout this paper, the main goal was to present the emergence of Network Analysis studies, subsequently the development of its mainstream core associated with social capital, and how the mainstream research responded to related criticism. At this section, I take in stock the debate above and discuss the extent that the mainstream has been able to respond to its critics, and the likely limits to its expansion.

The first theme discussed was the “Structural determinism” and “Structuralist instrumentalism” associated with Network Analysis studies. A related debate was the lack of attention to agency ( Borgatti & Halgin, 2011 ; Emirbayer & Goodwin, 1994 ). The mainstream response to critics has been to take agency to be strongly grounded on “rational choice” assumptions, thus, reinforcing what Emirbayer & Goodwin (1994) called “structuralist instrumentalism”. A full account of agency might encompass the idea of reflexivity and internal dialogue, as well as the interpretation of the concrete situation as fundamental (as seen above Emirbayer & Mische's (1998) , conception of human agency). An example of full engagement with the “structuralist constructionism” may be observed at McLean’s (2007) analysis of how enacted situations led to the deployment of rhetoric resources by Florentine families to reframe relationships.

The second theme debated was associated with the paucity or lack of meaning related to ties. A related debate was the dichotomy between forms and content. Mainstream scholars have made remarkable efforts in closing the gap established at the late eighties, where attention to ties’ content was shifted to the background (i.e. reintroduction of ethnography, development of multiplex models, etc.). The expansion of the possibilities of types of ties has also brought the reintroduction of negative ties that were present in earlier Network Analysis studies ( Labianca, 2014 ). As a byproduct, the belief that “connections are related to economic gains” has been revisited – social ties might also bring several types of “pains” ( Krackhardt, 1999 ). In contrast, recent qualitative studies, outside the social capital mainstream, have shown how standard questionnaires freeze the meaning attached to relationships, while these relationships’ would be better understood as outcomes of an ongoing process ( Small, 2017 ). Small’s (2017) research brings a direct implication for field researchers: to understand the meanings implied within one’s social network, it is not sufficient to apply questionnaires. Researchers must also deploy qualitative and unstructured methods to capture the process of formation and evolution of social ties.

Finally, the theme of temporality has risen as a source of criticism, and we have seen how mainstream has responded to it by distinguishing “relational events” from “relational states”, and then modeling the former without imposing “temporal granularity” assumptions to obtain the later. Also, researchers have improved their approach to modeling non-linear sequences of events. Yet, there is a standing challenge on how to grasp individual expectations of tie duration. In contrast, several scholars associated with “relational sociology” approaches have advocated thinking of ties as narratives. As such, ties should go beyond simple “existence” or “non-existence” at the present snapshot, to incorporate a full narrative description ( White, 2008 ). A narrative approach to networks would allow the qualitative collection of social ties without forcing the projection towards a single point in time.

This research bears the limitation of mainly focusing on mainstream management literature. As a consequence, there is a bias towards associating “social capital” to individual attainment. In contrast, future studies might expand the scope of investigation to cover empirical studies that focus on “collective social capital” ( Lazega, 2015 ).

Evolution of articles citing selected SNA concepts at top management journals

Percentage of articles citing selected SNA concepts at top management journals

Comparison between “social systems approach” and “social Capital approach” to SNA

Source: Author’s elaboration

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Open Access

Peer-reviewed

Research Article

Network analysis to evaluate the impact of research funding on research community consolidation

Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Visualization, Writing – original draft, Writing – review & editing

* E-mail: [email protected]

Affiliation University of California at Davis, Davis, California, United States of America

Roles Conceptualization, Data curation, Methodology, Writing – original draft, Writing – review & editing

Roles Conceptualization, Methodology, Writing – original draft, Writing – review & editing

• Daniel J. Hicks, 
• David A. Coil, 
• Carl G. Stahmer, 
• Jonathan A. Eisen

• Published: June 18, 2019
• https://doi.org/10.1371/journal.pone.0218273
• See the preprint
• Reader Comments

In 2004, the Alfred P. Sloan Foundation launched a new program focused on incubating a new field, “Microbiology of the Built Environment” (MoBE). By the end of 2017, the program had supported the publication of hundreds of scholarly works, but it was unclear to what extent it had stimulated the development of a new research community. We identified 307 works funded by the MoBE program, as well as a comparison set of 698 authors who published in the same journals during the same period of time but were not part of the Sloan Foundation-funded collaboration. Our analysis of collaboration networks for both groups of authors suggests that the Sloan Foundation’s program resulted in a more consolidated community of researchers, specifically in terms of number of components, diameter, density, and transitivity of the coauthor networks. In addition to highlighting the success of this particular program, our method could be applied to other fields to examine the impact of funding programs and other large-scale initiatives on the formation of research communities.

Citation: Hicks DJ, Coil DA, Stahmer CG, Eisen JA (2019) Network analysis to evaluate the impact of research funding on research community consolidation. PLoS ONE 14(6): e0218273. https://doi.org/10.1371/journal.pone.0218273

Editor: Wolfgang Glanzel, KU Leuven, BELGIUM

Received: February 1, 2019; Accepted: May 29, 2019; Published: June 18, 2019

Copyright: © 2019 Hicks et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: The MoBE article list is included with the data collection and analysis scripts at https://doi.org/10.5281/zenodo.2548840 . Data from Crossref can be retrieved using the available scripts. Data from Scopus cannot be shared publicly for intellectual property reasons, but can be retrieved using the available scripts at a subscribing institution.

Funding: Funding for DAC and JAE came from the Alfred P. Sloan Foundation. DJH’s postdoctoral fellowship was funded by a gift to UC Davis from Elsevier. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests: DJH’s postdoctoral fellowship was funded by a gift to UC Davis from Elsevier. This does not alter our adherence to PLOS ONE policies on sharing data and materials.

Introduction

In 2004, the Alfred P. Sloan Foundation launched a program focusing on the “Microbiology of the Built Environment”, sometimes known as “MoBE”. The aims of this program were to catalyze research on microbes and microbial communities in human built environments, such as homes, vehicles, and water systems; and to develop the topic into a whole field of inquiry. Prior to 2004, many new developments (e.g., major advances in DNA sequencing technology) had catalyzed innovation in studies of microbes found in other environments (e.g., those living in and on humans and other animals, those found in the soil, those found in the oceans), but these innovations had not spread rapidly enough to studies of the microbes in the built environment. Similarly, many developments had occurred in studies of the built environment (e.g., the spread of low cost sensor systems), but focus had not yet been placed on the living, microbial components of built environments. This is not to say there had been no studies on the MoBE topic prior to 2004, but rather that the pace of advances in the area were modest at best compared to advances in other areas of microbiology and built environment studies. The MoBE area was founded on the belief that institutionally supported, integrated, trans-disciplanary scientific inquiry could address these shortfalls and lead to major benefits in areas such as indoor health, disease transmission, biodefense, forensics, and energy efficiency.

The Sloan Foundation’s program ultimately lasted 15 years and invested more than $50 million on work in the MoBE field. A key goal of this program was to bring together the highly disparate fields of microbiology (especially the area focused on studies of entire ecosystems of microbes) and building science (e.g. with a focus on building, maintaining, regulating, and studying built environments) with their different approaches, cultures, incentives, and rewards. Grants were given to many projects and a diverse collection of people covering many fields including microbiology, architecture, building science, software development, and meeting organization (a list of all grants from the program can be found at https://sloan.org/grants-database?setsubprogram=2 ). The products of these grants included a diverse collection of programs and projects, dozens of new collaborations, many novel and sometimes large data sets on various MoBE topics, new software and tools for MoBE studies, and hundreds of scholarly publications.

Recent reviews of the state of the field (e.g. [ 1 ] [ 2 ]) have qualitatively highlighted the success of this program. In this paper we report a quantitative assessment of the Sloan MoBE program and the MoBE field using a network analysis of scholarly literature. Specifically, the aim of this study was to compare the community of researchers funded by the Sloan Foundation’s MoBE program to their scientific peers. If the Sloan Foundation’s program was successful at cultivating a new research community around MoBE topics, we hypothesized that we would see the evolution of an increasingly dense and more tightly connected network over the duration of the funding program.

Programs explicitly dedicated to funding interdisciplinary research may have an important role to play in the development of new research communities. [ 3 ] finds that interdisciplinary research proposals are less likely to be funded by the Australian Research Council’s Discovery Programme, which is designed to fund basic research across the disciplines but is not explicitly interdisciplinary. This indicates an incentive for researchers to propose—and then conduct—disciplinary research, which is more likely to build on established research communities. By contrast, [ 4 ] finds evidence of both novel collaborations as well as cross-disciplinary citations and publications for researchers funded by the US National Robotics Initiative program, which is explicitly interdisciplinary.

[ 5 ] proposes that coauthor networks can be used to examine the emergence of Kuhnian “normal science” [ 6 ]. Specifically, they relate the formation of a giant component—in which a single connected component of the network contains a supermajority of authors—to the formation of the kind of research community Kuhn described. [ 5 ] focuses on three topological statistics for coauthor networks: (1) the diameter (average shortest path length between pairs of nodes) of the largest component, (2) the fraction of edges in the largest component, and (3) “densification,” the exponent of a power law model relating edge and node counts across time for a given dynamic network. While diameter and edge fraction are dynamic, calculated at each time step (e.g., annually) as the coauthor network changes, densification is a summary across time. [ 7 ] uses topic modeling to subdivide papers from the arXiv, the physics repository, into various subfields, then applies the approach of [ 5 ] to examine the dynamics of coauthor networks in each subfield. Following [ 5 ], [ 7 ] also uses the diameter of the largest component as a key statistic, but also examines the fraction of nodes, rather than edges, in the largest component.

As [ 5 ] acknowledges, Kuhn’s notion of a paradigm and normal scientific research is controversial. In addition, network topology alone cannot provide insight into the normative aspects of a Kuhnian paradigm. That is, in Kuhn’s view, a paradigm provides a rules and standards for good scientific research. The term paradigm comes from linguistics, in which a paradigm characterizes rules and standards for a specific construction. For example, “amo, amas, amat, amamus, amatis, amant” is a paradigm for the first conjugation of Latin verbs. Similarly, the paradigms for a normal science (e.g., protocols for experimental design and statistical analysis) provide shared rules and standards for good research—at least for the research community operating under the paradigm. The fact that a network of researchers are working with each other does not tell us whether they have this kind of shared normative framework.

However, the fact that a network of researchers are working with each other (or not) does provide insight into the structural possibilities for the circulation of ideas and information among researchers. Information flow within and across the boundaries of scientific communities has long been a major topic in science and technology studies (STS) and philosophy of science [ 8 ]; [ 9 ]; [ 10 ]. Increased information flow is also often a key goal of research funding programs, especially information flow across disciplinary boundaries [ 11 ]. Insofar as a scientific community is defined in terms of information flow, a transition from a disconnected or loosely-connected collaboration network to a highly-connected one does provide evidence for the formation of a scientific community.

[ 12 ] moves from coauthor networks to institutional collaboration networks (if X and Y are coauthors, then their respective institutions are collaborators) to examine the development of the field of strategic management. [ 12 ] calculates several dynamic network statistics for institutional networks, including average clustering, diameter, “connectedness” and “fragmentation” (which unfortunately are not defined, and have various incompatible definitions in the network analysis literature), and the number and fraction of nodes in the largest component.

[ 13 ] examines the role of funded researchers (“PIs”) in the collaboration network in Slovenia from 1970-2016. Part of their analysis focuses on the relationship among several statistics over overlapping time periods, including the fraction of nodes in the giant component, the mean fraction of each node’s neighbors who are PIs, the number of connected components when PIs are removed from the giant component, and the relative size of the largest component when PIs are removed.

All of these studies use dynamic analysis of coauthor networks to examine development and change in research communities over time. However, none of these studies is designed to examine the effect of a particular funding program on the research community, and only [ 13 ] situates the group of researchers of interest (“PIs” or funded researchers) in the context of their peers (i.e., authors who were not funded).

In contrast, [ 14 ] uses coauthor and institutional collaboration networks, among other bibliometric methods, to examine the impact of a US National Aeronautics and Space Administration (NASA) program focused on astrobiology; while [ 15 ] uses a coauthor network, again among other methods, to study the early impacts of the US National Science Foundation (NSF) Science of Science Policy (SciSIP) program. Because these are early assessments of their respective funding programs, both of these studies use static rather than dynamic collaboration networks.

[ 16 ] and [ 17 ] use dynamic network methods to analyze individual-level funding program impacts. [ 16 ] compares participants in two fellowship programs, funded by Japan Science and Technology Agency and Japan Society for the Promotion of Science, to their peers in a large literature database, focusing on individual betweeness centrality over time. [ 17 ] tests several hypotheses concerning the relationship between local topological features of the network (e.g., the size of a researcher’s neighborhood) and patent applications under a Chinese program to fund photovoltaic research.

Of these four program assessment studies, only [ 16 ] incorporates a comparison group of researchers.

In the present study, we use the theoretically-informed approach developed in [ 5 ] and [ 7 ] to examine the community-level impact of a specific funding program, namely, the MoBE program. By comparing MoBE-funded researchers to their peers, and incorporating robustness checks for the way peers are identified, we can have more confidence in the interpretation of our results as identifying causal effects of the MoBE program. In addition, by deploying a wider variety of network statistics, we identify changes in the coauthor networks that would be missed by the smaller set of statistics used in [ 5 ] and [ 7 ].

Compared to the literature reviewed above, our study is distinctive for using network analysis methods and a comparison group of researchers to analyze the community-level impacts of a particular research funding program. To be clear, we make no claims here about the impacts of research funding programs more generally, but we do think that the MoBE program is an interesting case of an explicit attempt to create an interdisciplinary, multi-institution research community. Insofar as we find that the MoBE program was successful in this attempt, future research might identify specific features of the program that contributed to this success and could be generalized to other such programs.

Methods and materials

Corpus selection.

Publications funded by the Sloan Foundation’s MoBE program provided the starting point for our data collection and analysis. We evaluate the effect of this program by analyzing these publications in the context of previous work by the same authors, as well as a “control” or comparison set of authors working in the same general areas. We identify the comparison set as authors publishing frequently in the same journals as MoBE-funded publications.

Identifying sloan foundation-funded publications

A list of awards made within the Sloan-funded MoBE program is available at https://sloan.org/grants-database?setsubprogram=2 . The MoBE program awarded USD 51,000,000 in grants ranging from USD 3,500 to USD 2,500,000 (mean USD 335,000, median USD 125,000). Table 1 lists organizations than received 3 or more awards from this program. Fig 1 shows the number of new and active awards and publications within the MoBE program over time. While the earliest research awards were awarded in 2004, the number of new research awards expanded rapidly starting in 2011, with peak activity (most active research awards) in 2014. The first MoBE-funded publications did not appear until 2008, and peak publication occurred in 2016, indicating a lag of 2-3 years between research activities and the publication record.

• PPT PowerPoint slide
• PNG larger image
• TIFF original image

A: New awards made each year. B: Active awards in each year. C: Publications in each year. Dark gray vertical lines indicate the end of 2017, when MoBE-funded publications were identified. Colors indicate award types in A and B; color is not meaningful in C.

https://doi.org/10.1371/journal.pone.0218273.g001

Awards include research funding as well as funds for meeting organization, data infrastructure development, outreach, and other categories. n: Number of awards received.

https://doi.org/10.1371/journal.pone.0218273.t001

A list of publications associated with the MoBE program was compiled through a combination of strategies. An initial set of papers was identified by manually searching for acknowledgement of Sloan Foundation funding in any publications authored by the grantees during the program period. Additional publications were identified by searching Google Scholar for relevant MoBE papers and identifying those authored by grantees during the program period. Finally, each grantee (as well as sometimes their lab members (n = ~ 50)) was contacted directly and asked whether the publication list we had for them was both accurate and complete. This feedback led to some publications being removed from the list (as having not derived from the Sloan Foundation’s program) and others being added. In addition, we posted requests for feedback in various social media settings (e.g., blogs, Twitter) asking for feedback on the list ( https://www.microbe.net/2017/09/07/sloan-funded-mobe-reference-collection/ ; https://www.microbe.net/2018/03/15/one-last-call-for-help-with-sloan-funded-mobe-paper-collection/ ). The final list contained 327 publications. 20 of these publications did not have digital object identifiers (DOIs) on record and were excluded from further analysis.

Identifying peer authors

We sought to compare MoBE researchers to peers who were not funded by the MoBE program, in order to control for ordinary developments in both individual careers (e.g., more senior researchers are likely to have more collaborators) and research communities (e.g., more researchers are trained and join the community). In what follows, researchers funded by the Sloan Foundation’s program are referred to as the “collaboration” authors; their peers are the “comparison” authors.

Several methods were considered for developing this comparison set. Keyword searches were judged to be too noisy, producing significant numbers of false positive and false negative matches, as well as highly sensitive to the particular keywords used. Forward-and-backward citation searches using the 307 MoBE articles (compare [ 18 ]) produced lists on the order of 1,000,000 publications, which was judged to be impractically large. As an alternative, peer authors were identified as authors who are highly prolific in the same journals as the 307 MoBE articles.

Specifically, using the rcrossref package [ 19 ] to access the Crossref API (application programming interface; https://github.com/CrossRef/rest-api-doc ), metadata were retrieved for 572,362 articles published in 111 journals between 2008 and 2018 inclusive. ( PLOS One was dropped prior retrieving these metadata, due to its general nature and extremely high publication volume.) 14 journals published at least 10,000 articles during this time period; these appeared to be high-volume, general or broad-scope journals, such as Science or Environmental Science & Technology . The 345,546 articles from these 14 journals were removed, leaving 226,816 articles from 97 journals. Because Crossref does not provide any standardized author identifiers, simple name matching was used to estimate the number of articles published by each author. (This method means “Maria Rodriguez” and “M. Rodriguez” would be counted as different authors at this stage.) The same method was used to roughly identify authors of MoBE-funded papers. After filtering out authors of MoBE-funded papers, the 1,000 most prolific authors were selected as candidates for the comparison set. See Fig 2 .

https://doi.org/10.1371/journal.pone.0218273.g002

Next, to retrieve standardized author identifiers, a covering set of papers was identified such that each candidate name appeared as an author of at least one paper in the covering set. This covering set included all candidates by name, and no filtering was applied in identifying the covering set. Metadata for these papers was retrieved from the Scopus API ( https://dev.elsevier.com ), which incorporates an automated author matching system and standardized identifiers, referred to as author IDs. These author IDs were then used to characterize researchers as members of the MoBE collaboration or comparison set. Collaboration authors were defined as any author who either (a) was an author of at least two MoBE-funded papers or (b) was the author of at least one MoBE-funded paper and appeared in the candidates list (total n = 393 distinct names for the collaboration; 438 distinct author IDs). Candidates for the comparison set were removed if they were classified as part of the collaboration (total n = 770 distinct author IDs for the comparison set). (In what follows, we do not distinguish between authors and author IDs).

Author histories

Author histories (up to 200 publications since 1999 inclusive) for all 1,208 authors were retrieved using the Scopus API. These histories include both MoBE-funded and non-MoBE-funded papers, published in all journals indexed by Scopus. This resulted in an analysis dataset of 85,306 papers. Besides standard metadata, each paper was identified as MoBE-funded (or not). Table 2 shows the distribution of papers in the analysis dataset across 4 author combinations: only comparison authors; only collaboration authors, with separate counts for MoBE and non-MoBE funded papers; and “mixed” papers, with authors from both sets.

Author groups are based only on authors included in either the collaboration or comparison set. For example, a non-MoBE paper by two collaboration authors and a third author (not included in either the collaboration set or the comparison set) would be counted as “collaboration authors only”.

https://doi.org/10.1371/journal.pone.0218273.t002

Disciplinary identification

As discussed in the introduction, one of the primary aims of the MoBE program was to promote interdisciplinary collaboration between microbiologists, on the one hand, and researchers in fields such as civil engineering and indoor air quality, on the other. To assess the success of the program in this respect, we attempted to collect data on researchers’ disciplinary self-identification. We contacted 80 MoBE-funded researchers via email, asking them what percentage of their research/work they would consider related to microbiology, building science, or “other.” 30 researchers responded. We conducted an exploratory analysis, looking for associations between area self-identification and researchers’ publications in the analysis dataset, based on (a) the All Science Journal Classification [ASJC] subject areas identified by Scopus, (b) all words used in paper abstracts, and (c) the 1000 most-informative words used in paper abstracts (where “informative” was calculated in terms of entropy over the self-identified disciplines). In each case, principal component analysis indicated that there were no useful associations that could be used to classify all authors within this disciplinary space (e.g., using a machine learning model). In light of these unpromising exploratory results and limited resources, efforts to interdisciplinary collaboration were not pursued further.

Network analysis

The analysis dataset of 85,306 papers was used as the basis for constructing time-indexed collaboration networks. Each author forms a node (distinguished by author ID); edges correspond to papers published in a given year, so that two authors are connected by an edge for a given year if they coauthored at least one paper published in that year. All collaboration authors had at least one edge; 72 comparison authors did not have at least one edge (i.e., at least one paper coauthored with another author in the dataset), and were dropped from the network analysis (remaining comparison n = 698). Authors who collaborated on multiple papers in a given year were connected with multiple edges, except when calculating density (see below).

After constructing the combined (collaboration + comparison) network, separate cumulative-annual networks were constructed for each set of authors. For example, two authors would be connected in the 2011 network if and only if (1) they were in the same author set and (2) they had coauthored at least one publication between 1999 and 2011 inclusive. Cumulative networks were used to reduce noise in the most recent years, due to incomplete data for 2018 and as the Sloan Foundation’s funding program was starting to wind down. Analyzing separate cumulative networks allows the examination of the development of research communities through time and between the author sets.

For network analysis, we extended the approach developed by [ 5 ] and [ 7 ]. Specifically, both of these studies proposed that community formation can be measured in terms of giant component coverage and mean distance or shortest path length: increasing coverage combined with decreased distance indicates community consolidation. Neither [ 5 ] nor [ 7 ] used a control or comparison group (neither study aimed to to examine the impact of a specific funding program or other intervention). In the study, we calculated a total of eight network topological statistics and directly compare the two author sets. Specifically, we calculated the number of authors, number of components, coverage of the giant component (as a fraction of authors included in the largest component), entropy ( H ) of the component size distribution, diameter, density (fraction of all possible edges actually realized), mean distance, and transitivity in each year.

Number of authors simply measures the total size of each network. Because these are cumulative networks, the number of authors necessarily increases. The number of components, coverage of the giant component, and entropy of the component distribution are measures of the large-scale structure of the network. More components indicate that the network is divided into subcommunities that do not interact (at least in terms of coauthoring papers); fewer components indicates consolidation of the research community. Giant component coverage and entropy measure the relative sizes of these different components; higher giant component coverage and lower entropy indicate that more authors can be found in a single component, which in turn indicates research community consolidation.

Diameter, density, and mean distance can be interpreted as measures of the ability of information to flow through the network. Lower diameter, higher density, and lower mean distance indicate that it is easier for information to move between any two given researchers, as there are fewer intermediary coauthors and a higher probability of a direct connection. These therefore indicate research community consolidation.

Transitivity is an aggregate measure of the local-scale structure of the network. Low transitivity indicates that the network is comprised of loosely connected clusters; there is collaboration across groups of researchers, but it is relatively rare. High transitivity, by contrast, indicates that the network cannot be divided into distinguishable clusters. High transitivity therefore indicates research community consolidation.

Two robustness checks were incorporated into our analysis. First, to account for the possibility of data errors or missingness, perturbed networks were generated for each year by randomly switching the endpoints of 5% of edges. Second, the construction of the comparison set is likely to exclude students, postdoctoral researchers, and other early-career researchers. Insofar as these types of authors are included in the collaboration set, the collaboration network may appear to be more well-connected than the comparison set. To account for this possibility, we construct and analyze filtered versions of the annual cumulative networks. Authors are included in the filtered versions only if they have 50 or more papers total in the analysis analysis dataset.

Acknowledgment sections and other sources of funding information are not included in the metadata retrieved for this analysis. We are therefore unable to identify funding sources except for MoBE-funded papers, for which we have our own metadata. The comparison method is thus designed to test only whether or not the removal of MoBE-funded research produces a response effect in the shape of the overall discursive space. It does not consider independent relationships between MoBE and other sources nor relationships between non-MoBE sources. An underlying assumption of the analysis is, therefore, that the rates of impact from other sources of research funding are constant and that there is no underlying relationship between MoBE funding and other funding sources such that the removal of MoBE funding results in uneven removal of another source(s) of funding. Examining these relationships is potential direction for future study.

All data collection and analysis was carried out in R [ 20 ]. Complete data collection and analysis code, as well as the list of MoBE-funded publications, is available at https://doi.org/10.5281/zenodo.2548839 .

Results/Discussion

Qualitative analysis.

The development of the combined network is shown in Fig 3 . MoBE-funded authors and papers are shown in blue; non-MoBE-funded authors and papers are shown in red. All together, we believe that Fig 3 shows the consolidation of the MoBE collaboration within a consolidating larger research community.

Panels show time slices (non-cumulative) of the giant component of the combined coauthor network. Blue nodes and edges are MoBE authors and papers; red nodes and edges are non-MoBE authors and papers. Network layouts are calculated separate for each slice using the Fruchterman-Reingold algorithm with default values in the igraph package.

https://doi.org/10.1371/journal.pone.0218273.g003

Prior to the beginning of the MoBE funding in 2004, subset of MoBE researchers are actively working with each other; but many MoBE researchers are isolated in this network, and the largest component is only loosely connected. Qualitatively, the combined network has a sparse “lace” structure, with many long loops, as well as an “archipelago” of numerous small disconnected components.

During the early years of the funding period (2005-2008 and 2009-2013), a tighter cluster of MoBE researchers appears on the margins of the overall research community; but many MoBE researchers can be found scattered among the comparison authors and in disconnected components. The combined network has a “hairy ball” appearance, with a dense central “ball” and many peripheral “hairs,” and again an extensive “archipelago.” Part of the MoBE collaboration appears as a somewhat coherent “sub-ball.” We infer that this indicates that this part of the MoBE collaboration is highly integrated within the larger community.

During the peak period of MoBE funding (2015-2018), the vast majority of MoBE researchers appear to form one or two large, coherent communities at the center of the giant component—well-defined “blobs” of blue within a larger blob of red. Very few MoBE researchers appear outside of this coherent community. We suggest that this indicates tight integration involving almost all members of the MoBE collaboration.

However, because qualitative features of a visualized network are heavily dependent on the visualization method, this qualitative analysis should not be overinterpreted. Below we provide a quantitative analysis, less susceptible to overinterpretation.

Note that a few comparison set authors remain in small disconnected components even in the final time slice. These likely reflect “false positives” in the construction of the comparison set: authors who appear relatively frequently in the same journals as the MoBE publications, but do not actually conduct research in relevant research areas. We manually identified some such false positives, including authors of news stories in journals such as Current Biology or Nature Biotechnology as well as a few neuroscientists.

Quantitative analysis

Fig 4 shows statistics over time for the cumulative collaboration networks in each author set. Overall, both the MoBE research community and the comparison research community consolidated over time; but the MoBE research community consolidated faster and more thoroughly than the comparison set.

See text for explanation of the different statistics calculated here. Solid lines correspond to observed values; shaded ribbons correspond to 90% confidence intervals on rewired networks, where 5% of the observed edges are randomly rewired while maintaining each node’s degree distributions. 100 rewired networks are generated for each author set-year combination. Dashed lines correspond to observed values for authors with 50 or more total papers in the data. Blue corresponds to the MoBE collaboration; red corresponds to the peer comparison set of authors. Vertical lines indicate 2004, the first year of research funding by the MoBE program. Due to publication lags, we would not expect to see effects from 2004 funding until 2006-07.

https://doi.org/10.1371/journal.pone.0218273.g004

The most notable differences between the two author sets appear with the number of components, diameter, density, and transitivity. The comparison set stabilizes at 15-20 distinct components, while the MoBE collaboration approaches fewer than 5 components. However, for both author sets giant component coverage approaches 1 and H approaches 0, indicating that both networks contain a single giant component; the comparison set simply has several disconnected components with isolated researchers. As observed in the qualitative analysis, we believe this is plausibly due to “false negatives” in constructing the comparison set. The remaining statistics are generally robust to the inclusion of such “false negatives”.

Prior to 2010, the MoBE and comparison sets have a similar diameter: increasing during 1999-2005 as new researchers are added; then roughly stable until about 2010. Diameter remains above 10 for the comparison set, with a notable increase in 2008 followed by a decrease after 2013. By contrast, starting around 2010, the MoBE collaboration diameter is consistently less and decreasing.

However, diameter might be criticized as sensitive to network size. The relatively low diameter of the MoBE collaboration might be explained by the fact that this network has about half as many researchers as the comparison set.

Density and transitivity are automatically normalized against network size, and so avoid this potential confounder. For the collaboration set, transitivity peaks near 90% in 2012, indicating that at this time the connected components of the MoBE collaboration have almost no internal structure: everyone involved in the collaboration in 2012 is working directly with almost everyone else. Density plateaus at about 10% at this same time, and remains roughly stable over the remaining years of the study period. Transitivity and density then drop somewhat, but still remain remarkably high, indicating a highly interconnected research community even as the number of authors approaches its peak of just over 400. Transitivity is greater than 60% for both author sets in 2008-2009, but then diverges, dropping to around 50% in the comparison set by 2018. Density is consistently below about 2.5% for the comparison set throughout the entire study period.

Because of the delay between research and journal article publication, these network statistics provide a lagging indicator of community formation, of roughly 2-3 years. Taking this lag into account, our network analysis indicates that the MoBE research community consolidated around the period 2008-2010.

Shaded regions in Fig 4 indicate that most comparisons between the MoBE and comparison sets are robust to data errors. Diameter and number of components are somewhat more sensitive to possible data errors than the other statistics; but even here the comparison set statistics are consistently greater than the MoBE set statistics, indicating less consolidation in the comparison set.

The dashed lines in Fig 4 indicate that the comparisons are also robust to excluding early-career researchers. Other than the number of authors—which necessarily will decrease when authors are filtered—the only noteworthy effect of filtering is to increase the density of the collaboration network. There is no practical difference in the other statistics, especially for comparing the two networks of authors. Intuitively, filtering less productive authors is likely to remove less-connected authors from the margins of the network. These authors are less likely to provide important ties connecting otherwise separated communities.

Conclusions

Overall, we believe our results support the hypothesis that the Sloan Foundation-funded researchers consolidated as a community over the course of the program during 2008-2010. Whereas at the start of the program there were relatively few connections between researchers, especially across domains, by the end of our study period the network was dense and highly interconnected. In particular, while the Sloan Foundation-funded community was initially less connected than the control community it reached a similar level of consolidation by the end of the study period. This suggests to us that the program was successful in the stated goal of increasing collaboration between researchers.

We note that the most dramatic differences between the MoBE collaboration and the comparison set could not have been detected using the two statistics calculated by [ 7 ], namely, giant component coverage and mean distance. Giant component coverage approached unity for both networks, and the difference in mean distance was relatively small. Mean distance could also be criticized as too sensitive to network size. By contrast, the most striking differences in this case appeared in density and transitivity, which are automatically normalized for network size.

Acknowledgments

The authors would like to thank the many program grantees who assisted us in refining the list of publications. Also thanks to Julia Maritz for compiling the initial list of publications.

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• 16. Fujita M, Inoue H, Terano T. Evaluating funding programs through network centrality measures of co-author networks of technical papers. 2017 IEEE International Conference on Big Data (Big Data). IEEE; 2017.
• 20. R Core Team. R: A Language and Environment for Statistical Computing [Internet]. Vienna, Austria: R Foundation for Statistical Computing; 2018. Retrieved: https://www.R-project.org .

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Abstract: Understanding the complex relationships of biomarkers in diabetes is pivotal for advancing treatment strategies, a pressing need in diabetes research. This study applies Bayesian network structure learning to analyze the Shanghai Type 1 and Type 2 diabetes mellitus datasets, revealing complex relationships among key diabetes-related biomarkers. The constructed Bayesian network presented notable predictive accuracy, particularly for Type 2 diabetes mellitus, with root mean squared error (RMSE) of 18.23 mg/dL, as validated through leave-one-domain experiments and Clarke error grid analysis. This study not only elucidates the intricate dynamics of diabetes through a deeper understanding of biomarker interplay but also underscores the significant potential of integrating data-driven and knowledge-driven methodologies in the realm of personalized diabetes management. Such an approach paves the way for more custom and effective treatment strategies, marking a notable advancement in the field.

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New online two-day course: An introduction to social network analysis

We are pleased to announce a new two-day online course introducing techniques for analysis of social network data, with the National Centre for Research Methods (NCRM) and the ESRC Research Centre on Micro-Social Change, on 4-5 November 2024. Dr Paulo Serôdio explains descriptive methods of network analysis which can help us understand how networks and social relationships work in the context of social policy.

To prevent obesity or smoking initiation among teenagers, who should be targeted in an intervention? How can we contain the spread of an infectious disease under limited resources? Who should be vaccinated first in order to be most effective during vaccination shortages? How can we dismantle a terrorist organization, a drug distribution network or disrupt the communication flow of a criminal gang?

Social network analysis offers the theoretical framework and the appropriate methodology to answer questions like these by focusing on the relationships between and among social entities. Unlike transitional research methods, we shift the object of study from the individual as the unit of analysis, to the social relations that connect these individuals. A network is therefore a structure composed of units and the relationships that connect them. Network analysis is about the position of these units, the overall structure and how these affect the flow of information. 

The focus of the course is not so much on how to express these concepts formally through mathematics, but rather on how to use appropriate software to acquire measurements for these concepts in the data and use them rigorously in empirical hypothesis testing. The majority of the course will focus on descriptive methods of network analysis, but we will also discuss network-specific models and inferential methods for network analysis. 

The course covers: 

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• Manipulation of network data (matrix algebra and graph theory);
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• Network visualization.

Learning outcomes:

• Navigate the key areas of research in social networks; 
• Acquire knowledge of data collection and suitable data structures for analysing social networks; 
• Develop an understanding of social phenomena through the lenses of the social networks theory; 
• Learn how to operate software package for the analysis of social network data; 
• Learn how to use and interpret graph-theoretic and matrix algebra concepts with real-world data;
• Acquire the ability and comprehension to independently read scientific literature using social network analysis methodology;
• Learn the fundamentals of social network analysis to acquire the necessary proficiency to explore more advanced topics autonomously.

Pre-requisites:

Basic knowledge of Excel and data matrices.

Course Format:

2 full days (09:00 – 17:30 each day)

Dr Paulo Serôdio is a researcher at the Institute for Social and Economic Research, of the University of Essex. His research interests lie at the intersection of network analysis, computational social science and public health. His research projects have received funding from the Economic and Social Research Council and from the Independent Social Research Foundation. He is also affiliated with the Economic History Department of the University of Barcelona, the Paris Institute of Complex Systems, the Center for Organizational Sociology at Sciences Po and with the South East European Studies at Oxford. Before joining the University of Essex, he held research positions at Northeastern University, the University of Oxford and the University of Barcelona. 

You can find more information about his research at  www.pauloserodio.com .

The fee per teaching day is £35 per day for students / £75 per day for staff working for academic institutions, Research Councils and other recognised research institutions, registered charity organisations and the public sector / £250 per day for all other participants. In the event of cancellation by the delegate a full refund of the course fee is available up to two weeks prior to the course. NO refunds are available after this date. If it is no longer possible to run a course due to circumstances beyond its control, NCRM reserves the right to cancel the course at its sole discretion at any time prior to the event. In this event every effort will be made to reschedule the course. If this is not possible or the new date is inconvenient a full refund of the course fee will be given. NCRM shall not be liable for any costs, losses or expenses that may be incurred as a result of its cancellation of a course, including but not limited to any travel or accommodation costs. The University of Southampton’s Online Store T&Cs also continue to apply.

Website and registration: Introduction to Social Network Analysis – online (ncrm.ac.uk)

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Data were pooled using network random-effects models and expressed as mean differences (MDs) and 95% CIs. To display the results for outcomes on the same plot, standardized mean differences (SMDs, represented by blue squares) and pseudo 95% CIs (represented by black horizontal lines and proportionally scaled to the 95% CIs of the MDs) were calculated. 2HPP indicates 2-hour postprandial glucose; ALT, alanine aminotransferase (to convert to μkat/L, multiply by 0.0167); AST, aspartate aminotransferase (to convert to μkat/L, multiply by 0.0167); BMI, body mass index; FPG; fasting plasma glucose; FPI, fasting plasma insulin; GRADE, Grading of Recommendations Assessment, Development and Evaluation; HbA 1c ; glycated hemoglobin A 1c ; HDL-C, high-density lipoprotein cholesterol; HOMA-IR, homeostatic model assessment of insulin resistance; IHCL, intrahepatocellular lipid; LDL-C, low-density lipoprotein cholesterol; and WC, waist circumference.

a HDL-C result has been reversed for display purposes; that is, a negative MD would mean a positive improvement.

eTable 1. Search Strategy MEDLINE

eTable 2. Search Strategy EMBASE

eTable 3. Search Strategy Cochrane

eTable 4. PICOTS b Framework

eTable 5. Trial Characteristics

eTable 6. Loop-Specific Approach for Inconsistency

eTable 7. Design by Treatment Approach for Inconsistency

eFigure 1. Cochrane Risk of Bias Summary for All Included Trials

eFigure 2. Risk of Bias Proportion for All Included Trials

eFigure 3. Transitivity Analysis Box Plots Showing the Distribution of the Mean Age (Years) of the Trials Across the Available Direct Comparisons

eFigure 4. Transitivity Analysis Box Plots Showing the Distribution of the Study Length (Weeks) of the Trials Across the Available Direct Comparisons

eFigure 5. Transitivity Analysis Box Plots Showing the Distribution of the Sample Size of the Trials Across the Available Direct Comparisons

eFigure 6. Transitivity Analysis Box Plots Showing the Distribution of % Males of the Trials Across the Available Direct Comparisons

eFigure 7. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on Body Weight

eFigure 8. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on BMI

eFigure 9. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on Body Fat (%)

eFigure 10. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on Waist Circumference

eFigure 11. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on HbA1c

eFigure 12. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on Fasting Plasma Glucose (FPG)

eFigure 13. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on 2-hour Post-Prandial Glucose (2HPP)

eFigure 14. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on Fasting Insulin

eFigure 15. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on HOMA-IR

eFigure 16. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on LDL-C

eFigure 17. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on Non-HDL-C

eFigure 18. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on Triglycerides

eFigure 19. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on HDL-C

eFigure 20. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on Total Cholesterol

eFigure 21. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on SBP

eFigure 22. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on DBP

eFigure 23. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on IHCL

eFigure 24. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on ALT

eFigure 25. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on AST

eFigure 26. Network Analysis With GRADE Assessment of the Certainty of the Evidence Comparing LNCSBs, SSBs and Water on Uric Acid

eFigure 27. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With Body Weight

eFigure 28. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With BMI

eFigure 29. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With Body Fat %

eFigure 30. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With Waist Circumference

eFigure 31. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With HbA1c

eFigure 32. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With FPG

eFigure 33. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With 2h-PP

eFigure 34. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With FPI

eFigure 35. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With HOMA-IR

eFigure 36. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With LDL-C

eFigure 37. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With Non-HDL-C

eFigure 38. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With TGs

eFigure 39. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With HDL-C

eFigure 40. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With TC

eFigure 41. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With SBP

eFigure 42. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With DBP

eFigure 43. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With IHCL

eFigure 44. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With ALT

eFigure 45. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With AST

eFigure 46. Network Diagram for Randomized Controlled Trials Investigating the Association of the Substitution of LNCSBs for SSBs, Water for SSBs, and LNCSBs for Water With Uric Acid

eFigure 47. Comparison Adjusted Funnel Plot for Body Weight

eFigure 48. Comparison Adjusted Funnel Plot for BMI

eFigure 49. Comparison Adjusted Funnel Plot for Body Fat (%)

eFigure 50. Comparison Adjusted Funnel Plot for Fasting Insulin

eFigure 51. Comparison Adjusted Funnel Plot for Fasting Blood Glucose

eFigure 52. Comparison Adjusted Funnel Plot for LDL-Cholesterol

eFigure 53. Comparison Adjusted Funnel Plot for Non-HDL-Cholesterol

eFigure 54. Comparison Adjusted Funnel Plot for Triglycerides

eFigure 55. Comparison Adjusted Funnel Plot for HDL-Cholesterol

eFigure 56. Comparison Adjusted Funnel Plot for Total-Cholesterol

eFigure 57. Comparison Adjusted Funnel Plot for Systolic Blood Pressure

eData 1. Body Weight (Kg)

eData 2. BMI (kg/m2)

eData 3. Body Fat (%)

eData 4. Waist Circumference (cm)

eData 5. HbA1c (%)

eData 6. Fasting Blood Glucose (mmol/L)

eData 7. 2-Hour Post-Prandial Glucose (mmol/L)

eData 8. Fasting Plasma Insulin (pmol/L)

eData 9. HOMA-IR

eData 10. LDL-Cholesterol (mmol/L)

eData 11. Non-HDL-Cholesterol (mmol/L)

eData 12. Triglycerides (mmol/L)

eData 13. HDL-Cholesterol (mmol/L)

eData 14. Total-Cholesterol (mmol/L)

eData 15. Systolic Blood Pressure (mmHg)

eData 16. Diastolic Blood Pressure (mmHg)

eData 17. Intrahepatocellular Lipid/Liver Fat (SMD)

eData 18. Alanine Aminotransferase (U/L)

eData 19. Aspartate Aminotransferase (U/L)

eData 20. Uric Acid (mmol/L)

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McGlynn ND , Khan TA , Wang L, et al. Association of Low- and No-Calorie Sweetened Beverages as a Replacement for Sugar-Sweetened Beverages With Body Weight and Cardiometabolic Risk : A Systematic Review and Meta-analysis . JAMA Netw Open. 2022;5(3):e222092. doi:10.1001/jamanetworkopen.2022.2092

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Association of Low- and No-Calorie Sweetened Beverages as a Replacement for Sugar-Sweetened Beverages With Body Weight and Cardiometabolic Risk : A Systematic Review and Meta-analysis

• 1 Department of Nutritional Sciences, Temerty Faculty of Medicine, University of Toronto, Toronto, Ontario, Canada
• 2 Toronto 3D Knowledge Synthesis and Clinical Trials Unit, Clinical Nutrition and Risk Factor Modification Centre, St Michael's Hospital, Toronto, Ontario, Canada
• 3 Applied Human Nutrition, Mount Saint Vincent University, Halifax, Nova Scotia, Canada
• 4 Faculty of Medicine, School of Medicine, The University of Queensland, Brisbane, Australia
• 5 Department of Nutrition, Harvard T.H. Chan School of Public Health, Boston, Massachusetts
• 6 Department of Nutrition Sciences, The University of Alabama at Birmingham, Birmingham
• 7 Division of Endocrinology and Metabolism, Department of Medicine, St Michael’s Hospital, Toronto, Ontario, Canada
• 8 Li Ka Shing Knowledge Institute, St Michael’s Hospital, Toronto, Ontario, Canada
• 9 Department of Medicine, Temerty Faculty of Medicine, University of Toronto, Toronto, Ontario, Canada
• 10 Division of General Internal Medicine, Department of Medicine, McMaster University, Hamilton, Ontario, Canada
• 11 Department of Clinical Medicine, Aarhus University, Aarhus University Hospital, Aarhus, Denmark
• 12 Vuk Vrhovac University Clinic for Diabetes, Endocrinology and Metabolic Diseases, Merkur University Hospital, Zagreb, Croatia
• 13 University of Zagreb School of Medicine, Zagreb, Croatia
• 14 University of Osijek School of Medicine, Osijek, Croatia
• 15 Institute for Clinical and Experimental Medicine, Diabetes Centre, Prague, Czech Republic
• 16 Physicians Committee for Responsible Medicine, Washington, DC
• 17 Universitat Rovira i Virgili, Human Nutrition Department, Institut d'Investigació Sanitària Pere Virgili, Reus, Spain
• 18 Centro de Investigación Biomédica en Red de Fisiopatología de la Obesidad y Nutrición (CIBERObn), Instituto de Salud Carlos III, Madrid, Spain
• 19 College of Pharmacy and Nutrition, University of Saskatchewan, Saskatoon, Saskatchewan, Canada

Question   Are low- and no-calorie sweetened beverages (LNCSBs) as the intended substitute for sugar-sweetened beverages (SSBs) associated with improved body weight and cardiometabolic risk factors similar to water replacement?

Findings   In this systematic review and meta-analysis of 17 randomized clinical trials, LNCSBs as a substitute for SSBs were associated with reduced body weight, body mass index, percentage of body fat, and intrahepatocellular lipid, providing benefits that were similar to those of water, the standard-of-care substitution.

Meaning   The findings of this study suggest that over the moderate term, LNCSBs are a viable alternative to water as a replacement strategy in adults with overweight or obesity who are at risk for or have diabetes.

Importance   There are concerns that low- and no-calorie sweetened beverages (LNCSBs) do not have established benefits, with major dietary guidelines recommending the use of water and not LNCSBs to replace sugar-sweetened beverages (SSBs). Whether LNCSB as a substitute can yield similar improvements in cardiometabolic risk factors vs water in their intended substitution for SSBs is unclear.

Objective   To assess the association of LNCSBs (using 3 prespecified substitutions of LNCSBs for SSBs, water for SSBs, and LNCSBs for water) with body weight and cardiometabolic risk factors in adults with and without diabetes.

Data Sources   Medline, Embase, and the Cochrane Central Register of Controlled Trials were searched from inception through December 26, 2021.

Study Selection   Randomized clinical trials (RCTs) with at least 2 weeks of interventions comparing LNCSBs, SSBs, and/or water were included.

Data Extraction and Synthesis   Data were extracted and risk of bias was assessed by 2 independent reviewers. A network meta-analysis was performed with data expressed as mean difference (MD) or standardized mean difference (SMD) with 95% CIs. The GRADE (Grading of Recommendations Assessment, Development and Evaluation) system was used to assess the certainty of the evidence.

Main Outcomes and Measures   The primary outcome was body weight. Secondary outcomes were other measures of adiposity, glycemic control, blood lipids, blood pressure, measures of nonalcoholic fatty liver disease, and uric acid.

Results   A total of 17 RCTs with 24 trial comparisons were included, involving 1733 adults (mean [SD] age, 33.1 [6.6] years; 1341 women [77.4%]) with overweight or obesity who were at risk for or had diabetes. Overall, LNCSBs were a substitute for SSBs in 12 RCTs (n = 601 participants), water was a substitute for SSBs in 3 RCTs (n = 429), and LNCSBs were a substitute for water in 9 RCTs (n = 974). Substitution of LNCSBs for SSBs was associated with reduced body weight (MD, −1.06 kg; 95% CI, −1.71 to –0.41 kg), body mass index (MD, −0.32; 95% CI, −0.58 to –0.07), percentage of body fat (MD, −0.60%; 95% CI, −1.03% to –0.18%), and intrahepatocellular lipid (SMD, −0.42; 95% CI, −0.70 to –0.14). Substituting water for SSBs was not associated with any outcome. There was also no association found between substituting LNCSBs for water with any outcome except glycated hemoglobin A 1c (MD, 0.21%; 95% CI, 0.02% to 0.40%) and systolic blood pressure (MD, −2.63 mm Hg; 95% CI, −4.71 to −0.55 mm Hg). The certainty of the evidence was moderate (substitution of LNCSBs for SSBs) and low (substitutions of water for SSBs and LNCSBs for water) for body weight and was generally moderate for all other outcomes across all substitutions.

Conclusions and Relevance   This systematic review and meta-analysis found that using LNCSBs as an intended substitute for SSBs was associated with small improvements in body weight and cardiometabolic risk factors without evidence of harm and had a similar direction of benefit as water substitution. The evidence supports the use of LNCSBs as an alternative replacement strategy for SSBs over the moderate term in adults with overweight or obesity who are at risk for or have diabetes.

Sugar consumption has emerged as an important public health concern. The evidence on this concern derives largely from consumption of sugar-sweetened beverages (SSBs), with excess intake of SSBs associated with weight gain and downstream cardiometabolic complications. 1 - 4 Sugar-sweetened beverages have been identified as an important public health target. 5 , 6 It is unclear whether low- and no-calorie sweetened beverages (LNCSBs) as a replacement strategy for SSBs provide the intended benefits. Recent systematic reviews and meta-analyses 7 have shown an association between LNCSBs and a higher risk of the conditions that they are intended to prevent, such as weight gain, diabetes, and cardiovascular disease, in prospective cohort studies 8 and have reported inconsistent findings for weight loss and improvements in downstream cardiometabolic risk factors in randomized clinical trials (RCTs). 7 , 8 Biological mechanisms involving impaired sensory and endocrine signaling that was mediated by the sweet taste receptor 9 , 10 and changes to the microbiome 10 , 11 have been implicated in support of these observations.

Methodological considerations, however, have been raised that limit the inferences that can be drawn from these data. The available prospective cohort studies are at high risk for reverse causality. 12 - 14 Furthermore, the syntheses of RCTs do not fully account for the calories available to be displaced by LNCSBs, with caloric (eg, SSBs) and noncaloric (eg, water and placebo) comparators that are pooled together or with noncaloric comparators that are used as the sole comparator, leading to an underestimation of the outcome of LNCSBs. 12 - 14

The prevailing uncertainties have led to mixed recommendations from authoritative bodies. Neither the Dietary Guidelines for Americans nor Canada’s Food Guide supports the use of LNCSBs, and instead both recommend replacing SSBs with water. 5 , 6 The American Heart Association supports a narrow indication for LNCSBs, recommending that LNCSBs should be used as a replacement by only adults who are habitual consumers of SSBs, but emphasizing the use of water or an unsweetened alternative. 15 Similarly, diabetes associations in the UK, US, and Canada support LNCSBs insofar as they are used to displace calories from sugars and SSBs. 16 - 18 The European Association for the Study of Diabetes has not made any specific recommendations about low- and no-calorie sweeteners (LNCSs) or LNCSBs. 19 To update the recommendations of the European Association for the Study of Diabetes, the Diabetes and Nutrition Study Group commissioned the present systematic review and meta-analysis to summarize the evidence from RCTs of the association of LNCSBs, the most important source of LNCSs in a diet and a single food matrix, with intermediate cardiometabolic outcomes. 20 Because of the importance of the comparator in drawing inferences about LNCSBs, we conducted network meta-analyses rather than traditional pairwise meta-analyses to assess the association of LNCSBs with body weight and cardiometabolic risk factors in adults with and without diabetes. We used 3 prespecified substitutions: LNCSBs for SSBs (intended substitution with caloric displacement), water for SSBs (standard-of-care substitution with caloric displacement), and LNCSBs for water (reference substitution without caloric displacement).

This systematic review and network meta-analysis was conducted according to the Cochrane Handbook for Systematic Reviews of Interventions 21 and the Preferred Reporting Items for Systematic Reviews and Meta-analyses ( PRISMA ) reporting guideline. 22 The protocol is registered at ClinicalTrials.gov ( NCT02879500 ).

We searched Medline, Embase, and the Cochrane Central Register of Controlled Trials from inception through December 26, 2021. Briefly, for this search, we used variations of the exposure terms (LNCSBs and SSBs), outcome terms (adiposity, glycemia, blood lipids, blood pressure [BP], nonalcoholic fatty liver disease [NAFLD], and uric acid), and study design terms (randomized controlled trial, randomized, and placebo). The full search strategy is presented in eTables 1 to 3 in the Supplement . Manual searches of the reference lists of included studies and reviews were also performed.

eTable 4 in the Supplement shows the PICOTS (Population, Intervention, Comparator, Outcome, Time, and Study) framework. 22 We included RCTs of at least 2 weeks that investigated the association of LNCSBs, SSBs, and/or water with cardiometabolic risk factors. We excluded trials that had multimodal interventions, did not use comparator groups containing at least 1 of the other beverage interventions, included children and pregnant or breastfeeding women, or did not provide viable outcome data. Trials of LNCSs in fortified or nutrient-dense beverages (eg, milk and juice) were also excluded because of the presence of other nutrients.

Two independent reviewers (N.D.M. and R.Z.) extracted relevant data from each included report (eMethods in the Supplement ). Additional information was requested from study authors when necessary. Race and ethnicity data were not collected because the available data were not presented by these variables.

The same independent reviewers (N.D.M. and R.Z.) assessed risk of bias for each included RCT using the Cochrane risk-of-bias tool. 23 Five domains of bias were assessed: sequence generation, allocation concealment, blinding of participants and personnel, incomplete outcome data, and selective reporting. Disagreements between the reviewers were resolved by consensus.

The primary outcome was body weight. Secondary outcomes were other measures of adiposity (body mass index [BMI], which was calculated as weight in kilograms divided by height in meters squared; percentage of body fat; and waist circumference), glycemic control (glycated hemoglobin A 1c [HbA 1c ], fasting plasma glucose, 2-hour postprandial glucose during a 75-g oral glucose tolerance test, fasting plasma insulin [FPI], and homeostatic model assessment of insulin resistance), blood lipids (low-density lipoprotein cholesterol, non–high-density lipoprotein cholesterol, triglycerides, high-density lipoprotein cholesterol, and total cholesterol), BP (systolic BP and diastolic BP), measures of NAFLD (intrahepatocellular lipid [IHCL], alanine aminotransferase, and aspartate aminotransferase), and uric acid. Change differences were preferred over end differences. Missing variance data were calculated using established formulas. 21

This network meta-analysis was based on a frequentist framework and was conducted using the network suite of commands in Stata, version 15 (StataCorp LLC). We used change from baseline values from each study to calculate the mean differences (MDs) between treatments for each substitution (LNCSBs for SSBs, water for SSBs, and LNCSBs for water); otherwise, we used postintervention values (eMethods and eData 1-20 in the Supplement ). We performed random-effects network meta-analyses for each outcome to compare the 3 interventions (LNCSBs, SSBs, and water) simultaneously. Inconsistency was assessed in the direct, indirect, and network estimates. We assessed interstudy heterogeneity in the direct (pairwise) estimates using the Cochran Q statistic with quantification by the I 2 statistic, where I 2 ≥50% and P  < .10 were considered to be substantial interstudy heterogeneity. We measured incoherence in the network estimates using both local (loop-specific and side-splitting) and global (design-by-treatment interaction model) approaches. 24 - 26 If 10 or more trials were available, we conducted a priori subgroup analyses by age, study duration, type of design, disease status, risk of bias, and funding source. Indirectness was assessed in the indirect comparisons by evaluation of intransitivity across the pairwise comparisons comprising the indirect estimates for the study characteristics of age, study length, sample size, and percentage of male participants. Publication bias was assessed if 10 or more trial comparisons were available; we used comparison-adjusted funnel plots to assess funnel plot asymmetry. 24

We assessed the certainty of the evidence using the Grading of Recommendations Assessment, Development and Evaluation (GRADE) system. 20 , 27 - 30 Network estimates of RCTs and the direct and indirect estimates that composed these network estimates started at a high certainty of evidence but were downgraded by established criteria for risk of bias, inconsistency (incoherence), indirectness, imprecision, and publication bias (eMethods in the Supplement ).

Figure 1 shows the flow of the literature search and selection, and eFigures 27 to 46 in the Supplement show the network diagram for each outcome. We identified 4541 reports, of which 13 met the eligibility criteria. An additional 4 reports were found through manual searching. A total of 17 RCTs with 24 trial comparisons were included that assessed the association of the 3 prespecified substitutions with body weight, other measures of adiposity, and cardiometabolic risk. 31 - 47 These RCTs involved 1733 adult participants (mean [SD] age, 33.1 [6.6] years; 1341 women [77.4%] and 392 men [22.6%]) with overweight or obesity who were at risk for or had diabetes.

The Table and eTable 5 in the Supplement provide key trial characteristics. 31 - 47 Overall, the RCTs had a medium sample size, with a median (range) number of 72 (27-308) participants, and involved more women than men (23% men to 77% women). Most participants were younger (median [range] age, 34 [23-48] years) and had overweight or obesity (median [range] BMI, 31 [22-36]), with 9 trials 31 - 36 , 38 - 42 , 44 - 46 that included only participants with overweight and/or obesity and 1 trial 40 that included participants with type 2 diabetes.

Only 8 trials (11 comparisons) 31 , 32 , 35 , 37 , 38 , 43 - 45 , 47 reported the type of LNCS used in the LNCSBs: 7 comparisons for aspartame and 1 comparison each for aspartame and acesulfame potassium blend, saccharin, rebaudioside A, and sucralose. Overall, LNCSBs were a substitute for SSBs in 12 trials (n = 601 participants), 33 - 35 , 38 , 43 - 45 , 47 water was a substitute for SSBs in 3 trials (n = 429), 33 , 35 , 36 , 41 and LNCSBs were a substitute for water in 9 trials (n = 974). 31 , 33 , 35 , 37 , 39 , 40 , 42 , 46 The median (range) dosages were 1000 (250-2000) mL per day for LNCSBs, 1000 (250-1750) mL per day for SSBs, and 580 (250- 2000) mL per day for water.

Fifteen trials 32 - 46 had a parallel design, and 2 trials 31 , 47 had a crossover design. Most RCTs were conducted in Europe (n = 8) and North America (n = 6). The median (range) duration of follow-up was 12 (3-52) weeks. Eight trials 33 , 34 , 38 - 40 , 43 , 44 , 47 were funded by agencies (government, not-for-profit health agency, or university sources), 4 trials 36 , 37 , 42 , 46 were funded by industry, and 5 trials 31 , 32 , 35 , 41 , 45 were funded by a combination of agency and industry. We contacted the authors of 7 studies 31 , 32 , 34 , 35 , 38 , 44 , 45 for additional data, and the authors of 2 studies 34 , 38 provided additional data.

eFigures 1 and 2 in the Supplement provide the Cochrane risk-of-bias tool assessments. Eight trial comparisons 32 , 34 , 35 , 37 , 41 , 43 , 44 , 47 received an unclear risk-of-bias rating, and 11 comparisons 31 , 33 , 36 , 38 - 40 , 42 , 46 were rated as having a low risk of bias. No RCTs were identified as having a high risk of bias, with no evidence of serious summary risk of bias across the trials.

Figure 2 shows the network meta-analyses of the association of the intended substitution of LNCSBs for SSBs with body weight, other measures of adiposity, and cardiometabolic risk factors. This substitution was associated with reduced body weight (MD, −1.06 kg; 95% CI, −1.71 to –0.41 kg) and lower BMI (MD, −0.32; 95% CI, −0.58 to –0.07), percentage of body fat (MD, −0.60%; 95% CI, −1.03% to –0.18%), and IHCL (standardized MD [SMD], −0.42; 95% CI, −0.70 to –0.14). No other outcomes had significant differences.

Figure 3 shows the network meta-analyses of the association of the standard-of-care substitution of water for SSBs with body weight, other measures of adiposity, and cardiometabolic risk factors. Neither the primary outcome of body weight (MD, −0.01 kg; 95% CI, −0.95 to 0.98 kg) nor any of the secondary outcomes showed significant differences, although the direction of association favored water for most of the outcomes.

Figure 4 shows the network analyses of the association of the reference substitution of LNCSBs for water with body weight, other measures of adiposity, and cardiometabolic risk factors. Greater reduction in body weight (MD, −1.07 kg; 95% CI, −1.95 to −0.19 kg) was associated with LCSBs compared with water. Among secondary outcomes, water compared with LNCSBs was associated with lower level of HbA 1c (MD, 0.21%; 95% CI, 0.02% to 0.40%), and LNCSBs compared with water were associated with a greater decrease in systolic BP (MD, −2.63 mm Hg; 95% CI, −4.71 to −0.55 mm Hg). No secondary outcomes were affected.

Adverse events were reported in 4 trials, 33 , 36 , 43 , 44 including tiredness, mood swings, headaches, body aches, nausea, hospitalizations, and weight gain. In all cases, the adverse events were not observed, 43 , 44 deemed to be unrelated to the intervention, 33 or not severe enough to be of consequence. 36

eTables 6 and 7 in the Supplement show the loop-specific and the design-by-treatment assessment of inconsistency (incoherence) in the network estimates. No significant incoherence was observed by any approach across the 3 substitutions.

eFigures 7 to 26 in the Supplement provide the assessments of network, direct and indirect estimates, inconsistency (heterogeneity) in the direct estimates, and inconsistency (incoherence) between the direct and indirect estimates using side-splitting method. There was evidence of substantial heterogeneity ( I 2 ≥50%; P  < .10) in the direct pairwise estimates of the association of LNCSBs as a substitute for water with the primary outcome of body weight and secondary outcomes of waist circumference, HbA 1c , FPI, homeostatic model assessment of insulin resistance, and triglycerides. Incoherence was not significant for any comparison, but on visual inspection slight instability between direct and indirect measures was present for BMI, percentage of body fat, HbA 1c , fasting blood glucose, FPI, homeostatic model assessment of insulin resistance, low-density lipoprotein cholesterol, triglycerides, high-density lipoprotein cholesterol, total cholesterol, systolic BP, diastolic BP, IHCL, alanine aminotransferase, aspartate aminotransferase, and uric acid.

Because no outcome had 10 or more trials in all 3 comparisons, we did not conduct subgroup analyses.

eFigures 3 to 6 in the Supplement present the evaluation of intransitivity (a domain of indirectness) among the indirect comparisons by comparing the distribution of the potential effect modifiers across the available direct comparisons for age, study length, sample size, and percentage of males. The assumption of transitivity was met for all indirect comparisons as there was no overlap in the range between the pairwise comparisons.

eFigures 47 to 57 in the Supplement show the comparison-adjusted funnel plots for outcomes with 10 or more trial comparisons (body weight, BMI, percentage of body fat, FPI, fasting plasma glucose, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, triglycerides, total cholesterol, and systolic BP). Funnel plot asymmetry was not observed for any of the outcomes.

eFigures 7 to 26 in the Supplement include the GRADE assessment for the network meta-analysis. The certainty of the evidence for body weight was moderate for LNCSBs as a substitute for SSBs (small reduction; downgrade for imprecision), moderate for water as a substitute for SSBs (no difference; downgrades for inconsistency and imprecision), and low for LNCSBs as a substitute for water (small reduction; downgrades for inconsistency and imprecision). The certainty of the evidence for the adiposity and cardiometabolic outcomes was generally moderate, ranging from very low to high for each of the 3 substitutions (downgrades for inconsistency, imprecision, and/or indirectness) and with nearly all directions of the association favoring the use of LNCSBs or water as a substitute for SSBs (small to trivial reductions) and diverging for the use of LNCSBs as a substitute for water (small to no differences).

In the present systematic review and meta-analysis, the use of LNCSBs as a substitute for SSBs was associated with reduced body weight, BMI, percentage of body fat, and IHCL, whereas the use of water as a substitute for SSBs was associated with no significant improvements, although the direction of association favored water in all cases. Furthermore, neither LNCSBs nor water as a substitute for SSBs was associated with significant improvements in glycemic control, BP, uric acid, or other aspects of the lipid profile or NAFLD markers, but the directions of the association favored LNCSBs or water in nearly all cases. The use of LNCSBs as a substitute for water did not show significant differences, except for a greater decrease in HbA 1c seen with water and in body weight and systolic BP seen with LNCSBs.

The findings in this study are in agreement with those reported in other systematic reviews and meta-analyses, 48 - 51 which have allowed for the interpretation of results by comparator. Specifically, the findings that (1) reduced body weight, BMI, and body fat were associated with the use LNCSBs as a substitute for SSBs with caloric displacement and (2) neutral outcomes were associated with the use of LNCSBs as a substitute for water without caloric displacement are consistent with the results of other systematic reviews and meta-analyses of RCTs. 48 - 51

Decreases in body weight, 48 , 49 body weight and BMI, 50 and a composite of body weight or BMI 51 were observed with the substitution of LNCSs for a caloric comparator (sugars in foods or beverages) predominantly in participants with overweight or obesity. Miller and Perez 50 further showed reductions in fat mass and waist circumference. Similarly, Toews et al 7 found small reductions in BMI with sucrose in foods or beverages as the caloric comparator in predominantly healthy participants. On the other hand, undifferentiated analyses by Toews et al 7 of the outcome of substituting LNCSs for a combination of caloric and noncaloric comparators and another analysis by Azad et al 8 that restricted the outcome of substituting LNCSBs for matched noncaloric comparators (placebo, water, or weight loss diet) found no differences in body weight with LNCSs predominantly in participants with overweight or obesity. Overall, these findings are consistent with the mechanism of LNCSBs being associated with weight loss insofar as they were a factor in reducing net energy intake.

The observed improvements in downstream, intermediate cardiometabolic outcomes are also in agreement with findings of previous systematic reviews and meta-analyses. In addition to their association with weight gain, 52 fructose-containing sugars that provide excess calories, especially in beverage form, have been associated with increased triglycerides, 53 , 54 glucose, 55 insulin, 55 uric acid, 56 and NAFLD markers. 57 Toews et al 7 showed that the use of LNCSs as a substitute for caloric sugars (sucrose) were a factor in reduced BP, and the reductions seen in IHCL would be expected through displacement of calories from SSBs.

The findings of this study can inform guidance on the role of LNCSBs in sugar-reduction strategies. There has been a particular focus on SSBs as the most important source of added or free sugars in several countries, 58 - 60 given that the overconsumption of sugar has been associated with weight gain, diabetes, and downstream complications of hypertension and coronary heart disease. 1 - 4 Although water is considered to be the standard-of-care substitution for SSBs by authoritative bodies, 5 , 6 , 15 - 19 with many health organizations recommending against the use of LNCSBs, the existing evidence confirms the intended benefits of LNCSBs as a substitute for SSBs over the moderate term. For habitual consumers of SSBs with overweight or obesity, who are at risk for or have type 2 diabetes, and who are unable to switch to water, LNCSBs may provide a viable alternative. This finding is particularly important given that most people in the National Weight Control Registry who are successful at weight loss maintenance consume LNCSBs and report that LNCSBs help in controling caloric intake and weight loss maintenance. 61

There is a need for high-quality RCTs that focus on quantifying the outcome of LNCSBs using different LNCS blends as substitutes for SSBs compared with the outcome of water (the standard-of-care substitution). We await the results of the STOP Sugars NOW (Strategies to Oppose Sugars With Non-nutritive Sweeteners or Water) trial and other similar RCTs to help clarify the role of LNCSBs. Future research using a range of designs is warranted to confirm whether the intended benefits of using LNCSBs as a substitute for SSBs are durable and extend to hard clinical outcomes.

This systematic review and meta-analysis has several strengths. First, the use of network meta-analysis allowed for the simultaneous assessment of the 3 prespecified substitutions (LNCSBs for SSBs, water for SSBs, and LNCSBs for water), leveraging direct and indirect comparisons with a common comparator to increase the information size. Undertaking a network meta-analysis rather than a regular pairwise meta-analysis provided 2 distinct advantages: (1) more precise estimates than single direct or indirect estimates, and (2) the ability to compare interventions that had not been compared before. Second, a comprehensive literature search that included only RCTs provided the greatest protection against bias, no evidence of serious risk of bias among the included trials, and use of the GRADE approach to assess the certainty of the estimates.

This systematic review and meta-analysis also has several limitations. First, evidence of inconsistency was present in the primary outcome of body weight across the substitutions of water for SSBs and LNCSBs for water and in several secondary outcomes across the 3 prespecified substitutions, resulting in downgrades for serious inconsistency. This inconsistency was associated with either unexplained heterogeneity in the direct estimates or incoherence from the difference between direct and indirect estimates. Network estimates closely followed the direct estimate, with indirect estimates improving precision when coherent and only trivially affecting network estimates when incoherent. Second, there was evidence of serious indirectness in several of the analyses. Only 1 RCT of direct comparisons was available for several secondary outcomes, limiting generalizability and leading to downgrades for serious indirectness. The moderate median follow-up duration of 12 weeks was considered to be another potential source of indirectness across the analyses. Although there is some uncertainty about whether the benefits and lack of harm associated with LNCSBs extended beyond the 12-week median follow-up, any harm may have manifested within this time frame. The analyses also included RCTs with up to 1 year of follow-up that showed no evidence of harm or even benefit. 33 , 42 Other large RCTs in children and adolescents (which were not captured in the present analyses) offer further evidence of durable benefit. 62 , 63 Therefore, we did not downgrade the evidence for the lack of long-term follow-up as a source of indirectness and instead made all conclusions specific to the moderate term. Third, there was evidence of serious imprecision in several of the pooled estimates. The 95% CIs crossed the prespecified minimal important differences for the primary outcome of body weight and several secondary outcomes across the 3 prespecified substitutions. Balancing the strengths and limitations, we assessed the certainty of the evidence as generally low to moderate for most outcomes.

In this systematic review and meta-analysis, using LNCSBs as an intended substitute for SSBs appeared to be associated with reductions in body weight and cardiometabolic risk factors, including BMI, percentage of body fat, and IHCL, without evidence of harm. These small improvements were similar in direction to those associated with water substitution, the standard of care. The evidence provides a good indication of the benefits of LNCSBs as an alternative replacement strategy over the moderate term for SSBs in adults with overweight or obesity who are at risk for or have diabetes.

Accepted for Publication: January 20, 2022.

Published: March 14, 2022. doi:10.1001/jamanetworkopen.2022.2092

Open Access: This is an open access article distributed under the terms of the CC-BY License . © 2022 McGlynn ND et al. JAMA Network Open .

Corresponding Author: John L. Sievenpiper, MD, PhD, St Michael's Hospital, #6138-61 Queen St E, Toronto, ON M5C 2T2, Canada ( [email protected] ).

Author Contributions : Ms McGlynn and Dr Sievenpiper had full access to all of the data in the study and take responsibility for the integrity of the data and the accuracy of the data analysis.

Concept and design: McGlynn, Khan, Jeppesen, Sievenpiper.

Acquisition, analysis, or interpretation of data: McGlynn, Khan, Wang, Zhang, Chiavaroli, Au-Yeung, Lee, Noronha, Comelli, Blanco Mejia, Ahmed, Malik, Hill, Leiter, Agarwal, Rahelić, Kahleova, Salas-Salvadó, Kendall, Sievenpiper.

Drafting of the manuscript: McGlynn, Khan, Wang, Zhang, Sievenpiper.

Critical revision of the manuscript for important intellectual content: McGlynn, Khan, Chiavaroli, Au-Yeung, Lee, Noronha, Comelli, Blanco Mejia, Ahmed, Malik, Hill, Leiter, Agarwal, Jeppesen, Rahelić, Kahleova, Salas-Salvadó, Kendall, Sievenpiper.

Statistical analysis: McGlynn, Khan, Zhang, Chiavaroli, Au-Yeung, Comelli.

Obtained funding: McGlynn, Sievenpiper.

Administrative, technical, or material support: McGlynn, Khan, Lee, Blanco Mejia, Hill, Agarwal, Rahelić.

Supervision: Khan, Jeppesen, Kendall, Sievenpiper.

Conflict of Interest Disclosures: Ms McGlynn reported receiving a Canadian Institutes of Health Research (CIHR)-Masters Award during the conduct of the study and being a former employee of Loblaws Companies Limited outside the submitted work. Dr Khan reported receiving grants from CIHR, International Life Science Institute, and National Honey Board outside the submitted work. Dr Chiavaroli reported being a Mitacs Elevate postdoctoral fellow and receiving joint funding from the Government of Canada and the Canadian Sugar Institute. Mr Au-Yeung reported receiving personal fees from Inquis Clinical Research outside the submitted work. Ms Lee reported receiving graduate scholarship from CIHR and the Banting & Best Diabetes Centre at the University of Toronto outside the submitted work. Dr Comelli reported being the Lawson Family Chair in Microbiome Nutrition Research at the Joannah and Brian Lawson Centre for Child Nutrition, University of Toronto, during the conduct of the study and receiving nonfinancial support from Lallemand Health Solutions, donation to research program from Lallemand Health Solutions, personal fees from Danone, sponsored research and collaboration agreement from Ocean Spray, and nonfinancial support from Ocean Spray outside the submitted work. Ms Ahmed reported receiving scholarship from the Toronto Diet, Digestive tract, and Disease Centre (3D) outside the submitted work. Dr Malik reported receiving personal fees from the City and County of San Francisco, Kaplan Fox & Kilsheimer LLP, and World Health Organization outside the submitted work and support from the Canada Research Chairs Program. Dr Hill reported receiving personal fees from General Mills and McCormick Science Institute. Dr Rahelić reported receiving personal fees from the International Sweeteners Association, Abbott, AstraZeneca, Boehringer Ingelheim, Eli Lilly, Novo Nordisk, Merck, MSD, Salvus, and Sanofi outside the submitted work. Dr Salas-Salvadó reported receiving personal fees from Instituto Danone Spain, nonfinancial support from Danone Institute International, personal fees as director of the World Forum for Nutrition Research and Dissemination from the International Nut and Dried Fruit Council Foundation, financial support to the institution from Fundación Eroski, and financial support to the institution from Danone outside the submitted work. Dr Kendall reported receiving grants and/or in-kind support from Advanced Food Materials Network, Agriculture and Agri-Food Canada, CIHR, Almond Board of California, Barilla, Canola Council of Canada, International Nut and Dried Fruit Council, Peanut Institute, Pulse Canada, Tate and Lyle Nutritional Research Fund at the University of Toronto, and Unilever; receiving nonfinancial support from General Mills, Kellogg, Loblaw Brands Limited, Oldways Preservation Trust, Quaker Oats (Pepsi-Co), Sun-Maid, White Wave Foods/Danone, International Pasta Organization, California Walnut Commission, Primo, Unico, International Carbohydrate Quality Consortium (ICQC), and Toronto Diet, Digestive tract, and Disease Centre (3D) outside the submitted work; receiving personal fees from McCormick Science Institute and Lantmannen; and being a member of the Diabetes and Nutrition Study Group (DNSG) Executive Board and Dietary Guidelines, a member of the expert committee of the DNSG Clinical Practice Guidelines for Nutrition Therapy, a member of the scientific advisory board of the McCormick Science Institute, a scientific advisor for the International Pasta Organization and Oldways Preservation Trust, a member of the ICQC, an executive board member of the DNSG, and being the director of the Toronto Diet, Digestive tract, and Disease Centre (3D) Knowledge Synthesis and Clinical Trials Foundation. Dr Sievenpiper reported receiving nonfinancial support from DNSG of the European Association for the Study of Diabetes (EASD), grants from CIHR through the Canada-wide Human Nutrition Trialists' Network (NTN), PSI Graham Farquharson Knowledge Translation Fellowship, Diabetes Canada Clinician Scientist Award, CIHR Institute of Nutrition, Metabolism and Diabetes and the Canadian Nutrition Society (INMD/CNS) New Investigator Partnership Prize, and Banting & Best Diabetes Centre Sun Life Financial New Investigator Award during the conduct of the study; receiving grants from American Society for Nutrition, International Nut and Dried Fruit Council Foundation, National Honey Board (the US Department of Agriculture [USDA] honey checkoff program), Institute for the Advancement of Food and Nutrition Sciences (IAFNS; formerly ILSI North America), Pulse Canada, Quaker Oats Center of Excellence, United Soybean Board (the USDA soy checkoff program), Tate and Lyle Nutritional Research Fund at the University of Toronto, Glycemic Control and Cardiovascular Disease in Type 2 Diabetes Fund at the University of Toronto (a fund established by the Alberta Pulse Growers), and Nutrition Trialists Fund at the University of Toronto (a fund established by an inaugural donation from the Calorie Control Council); receiving personal fees from Dairy Farmers of Canada, FoodMinds LLC, International Sweeteners Association, Nestlé, Abbott, General Mills, American Society for Nutrition, INC Nutrition Research and Education Foundation, European Food Safety Authority, Nutrition Communications, International Food Information Council, Calorie Control Council, Comité Européen des Fabricants de Sucre, International Glutamate Technical Committee, Perkins Coie LLP, Tate and Lyle Nutritional Research Fund at the University of Toronto, Danone, Inquis Clinical Research, Soy Nutrition Institute, and European Fruit Juice Association outside the submitted work; serving on the clinical practice guidelines expert committees of Diabetes Canada, EASD, Canadian Cardiovascular Society, and Obesity Canada/Canadian Association of Bariatric Physicians and Surgeons; being an unpaid scientific advisor for the Food, Nutrition, and Safety Program and the Technical Committee on Carbohydrates of IAFNS; being a member of the ICQC, executive board member of the DNSG of the EASD, and director of the Toronto Diet, Digestive tract, and Disease Centre (3D) Knowledge Synthesis and Clinical Trials Foundation; his spouse is an employee of AB InBev. No other disclosures were reported.

Funding/Support: This study was commissioned by the DNSG of the EASD, which provided funding and logistical support for meetings as part of the development of the EASD Clinical Practice Guidelines for Nutrition Therapy. This study was also supported by grant 129920 from CIHR through the Canada-wide NTN. The Toronto Diet, Digestive tract, and Disease Centre (3D), funded through the Canada Foundation for Innovation and the Ministry of Research and Innovation’s Ontario Research Fund, provided the infrastructure for the conduct of this project. Ms McGlynn was supported by a CIHR-Masters Award and a Research Training Centre scholarship from St Michel’s Hospital. Dr Comelli was funded from holding the Lawson Family Chair in Microbiome Nutrition Research at the University of Toronto. Dr Salas-Salvadó was funded by the ICREA (Catalan Institution for Research and Advanced Studies) Academia program. Dr Sievenpiper was funded by a PSI Graham Farquharson Knowledge Translation Fellowship, Diabetes Canada Clinician Scientist Award, CIHR INMD/CNS New Investigator Partnership Prize, and a Banting & Best Diabetes Centre Sun Life Financial New Investigator Award.

Role of the Funder/Sponsor: The Clinical Practice Guidelines Committee of the DNSG of the EASD had input on all aspects of this work. Other funders had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; and decision to submit the manuscript for publication.

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Computational analysis of knowledge and complexity trends in educational technology research titles from 1927 to 2023

• Published: 27 June 2024

Cite this article

• Shesen Guo 1 &
• Ganzhou Zhang 1  

This study looked at titles of research papers on educational technology that were published between 1927 and 2023 using computational text analysis. To map research trends, metrics for technology terminology use, network complexity, and knowledge updating rates were used. The findings showed that, despite some fluctuations, titles have become more technologically diverse and interconnected over time, indicating a greater emphasis on technology and interdisciplinarity. Escalating title complexity was visualized using network analysis. Citation patterns revealed that science/engineering and educational technology both update knowledge at comparable rates. This computational analysis shows how the fields of education and technology have been evolving together over time, giving historical context to understand current trends. The study shows how to use data science techniques to map the dynamics of research within a practical domain that connects technology and practice.

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Guo, S., Zhang, G. Computational analysis of knowledge and complexity trends in educational technology research titles from 1927 to 2023. Educ Inf Technol (2024). https://doi.org/10.1007/s10639-024-12815-8

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