The network approach to psychopathology: A theoretical framework

The central idea behind the network approach to psychopathology is that mental disorders arise from casual interactions between symptoms, where causality must be interpreted in the sense of the interventionist theory, according to which the relation between two symptoms is causal if there exists a possible (natural or experimental) intervention on one of them that changes the probability distribution of the other, independently of the how the causal relationships are triggered [6].

In order to represent and study these symptom-symptom interactions, a network structure can be used, a so-called symptom network. In the scientific setting, the term network refers to a mathematical structure called graph, which consists of a set of nodes connected by links, or, in more formal terms, an ordered pair G = (V, E) where V is the set of vertices (or nodes), i.e., the system’s components, and E is the set of edges (or links), i.e., the interactions between them. If the edges have no direction, thus indicating a two-way relationship, then the graph is said to be undirected; otherwise, if the edges are given a specific direction, that is, they can only be traversed in a single direction, then the graph is called directed. Moreover, each edge can also be given a number called weight, that represents a quantification of its strength or cost or capacity, according to the different context. In this case, the graph is said to be weighted to distinguish it from the unweighted type [8]. The arrangement of the network’s elements is called topology.

Although no distinction is usually made, the terminology “graph”, “vertex”, “edge” refers more precisely to the mathematical representation of the system, whereas “network”, “node”, “link” is more common in reference to real systems such as physical, biological, social, and economical systems. The network approach has proven successful and useful in a number of fields, from social sciences to economics, informatics, ecology, epidemics, biology, and medicine, among others (cfr. [9–14]). In the specific case of symptom networks, nodes encode symptoms and edges stand for causal influence between pairs of symptoms.

There might also be conditions that can change the state of symptoms from the outside of the psychopathology network, for example adverse life events, abnormal brain functioning and inflammation, among others; all together, these constitute the external field of the symptom network [6]. Another crucial property is the existence of partially overlapping syndromic clusters or bridge symptoms, that is, symptoms that are associated with multiple disorders and thus are part of symptom networks corresponding to different psychopathologies. This feature allows for an immediate explanation of the high level of comorbidity that characterizes mental disorders [5–7,15].

An ultimate facet that needs to be considered to complete the theoretical framework of network analysis applied to psychopathology is the proven existence (in most psychopathology networks) of a phenomenon called hysteresis, which is a fundamental indicator of the dynamics of the system and consists in the dependence of any state of the system to its history [16]. In other words, once a system has been activated by an external event, the subsequent fading of that event will not necessarily deactivate that symptom in case there exist connections with other symptoms that are strong enough to make the reactions provoked by the triggering event (i.e., the activated symptoms system) self-sustaining [6]. As proven by Cramer [16], the hysteresis effect becomes more pronounced as the connectivity of a network increases. In fact, what has been noticed is that in weakly connected networks, even though significant triggering events can cause strong reactions, once the event is over, the system will gradually recover and return to its asymptomatic state. In this sense, a weakly connected network is said to be resilient, as opposed to the vulnerable disposition of the strongly connected ones [6].

Following these observations, Borsboom [6] proposed new definitions of mental health as the stable state of a weakly connected network and mental disorder as an alternative stable state of a strongly connected network which is separated from the healthy state by hysteresis.

At this point, it is important to underlie that the conceptualization of the network approach to mental disorders should not be regarded as a theoretical finding only. Indeed, it has remarkable implications for the diagnosis and treatment systems as well [6,17].

The psychometric network analysis workflow

The term psychometric network analysis is used to describe the combined procedure of network estimation, network description and network stability analysis, which together build the bulk of the methodology used in network approaches to multivariate psychometric data [3,15,18–20].

The complete workflow (Fig 3) typically starts with a specific research question, according to which a suitable data collection scheme is chosen. Usually, experimental data is given in the form of either a cross-sectional, time-series or panel design. Although the subsequent procedures are generic statistical ones and thus apply to input variables of any kind, in this context psychometric variables usually consist of responses to questionnaire items, symptom ratings and cognitive test scores together with other possible personal or psychological indicators [18].

Download:

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

Fig 3. Psychometric network analysis workflow.

Scheme of the typical workflow of psychometric network analysis. Once the research question has been defined (also according to the availability of data), the main steps to be performed are: 1. Network estimation, that is, construction of the network. 2. Network description, that is, identification of important symptoms. 3. Network stability analysis, that is, assessment of the robustness of results. Together, these will allow to infer significant interpretation that should be employed in clinical treatment.

https://doi.org/10.1371/journal.pone.0276341.g003

Once enough data are available, the network estimation step can be carried out with the aim of approximating the values of links between pairs of nodes (i.e., the causal influence of one onto the other) and building an appropriate network structure at the system level. Depending on the peculiarities of the data, different statistical methods can be employed: the most frequent approach is that of assessing the edge parameters as conditional associations between variables to estimate the corresponding Pairwise Markov Random Field (PMRF), but the alternative strategy of Bayesian network estimation has been successfully employed as well [5]. Importantly, this step also encompasses the process of node selection and edge selection, the latter via general statistical methods such as fit indices, null-hypothesis testing, or cross-validation procedures.

The result of this step is generally a nontrivial topological structure which becomes the main subject of the network description phase, whose aim is to give a complete characterization of the symptom network with a particular focus on its most important nodes. Here, “importance” has to be intended as how a node is interconnected with the other nodes of the network and is commonly assessed by different centrality measures [5], that is, scalar values assigned to each node within a graph in order to assess their significance based on certain definitions of importance. In general, the tools of network analysis are employed to estimate network density and connectivity through global topological properties, node centrality through local topological properties and more fine-grained structural patterns such as communities and motifs (i.e., mesoscopic level [21]).

Next, it is fundamental to evaluate the stability and robustness of the estimated network and of the centrality indices. In fact, the estimation error and the sampling variation need to be considered in order to not obtain misleading results [22–26]. Altogether, the methods used to assess the accuracy of the estimated parameters and their ability to replicate in a different dataset constitute the network stability analysis [25].

Finally, the psychometric network analysis approach comes to an end with proper inferences which require taking into account both substantive domain knowledge and methodological considerations about the stability and robustness of the estimated network [18].

The clinical implications of such findings concern both the diagnosis and treatment systems. With respect to diagnosis, the network approach suggests clinicians to follow a two-step process according to which they should firstly identify the exhibited symptoms and then the network interactions that sustain them, which however is actually not very different from the current DSM diagnostic practice [6]; the novelty introduced by this approach is that it can help recognize the most important symptoms as well as other psychological traits that are not included in the DSM criteria [27], such as feeling ineffective and social insecurity in case of EDs. As for the treatment of the diagnosed disorder, the network perspective suggests clinicians to apply techniques that can change or manipulate the network, in particular that are capable of: changing the state of one or more symptoms, modifying the external field by removing triggering events or manipulating the network structure by altering the connections among symptoms [6]

Aim of the systematic review

The aim of this study is to collect and review the existing literature on psychometric network analysis of EDs. To the best of our knowledge, three other reviews centered on the application of this approach to EDs have already been published between 2018 and 2021 [28–30]. As already pointed out in [30], although giving important insights into the framework and potentialities of the network research on EDs, Levinson et al., 2018 [28] and Smith et al., 2018 [29] suffer from the limitation of reviewing only a restricted number of studies (3 and 5, respectively). On the other hand, the most recent review paper [30] examines a wider range of articles (i.e., 25) and precisely discusses their results, but leaves out an accurate analysis of the methodologies employed by the researchers. In addition, as already pointed out by the authors, a noteworthy limitation of this latter review is that no study based on longitudinal data was taken into consideration. With this systematic review, we intend to update and broaden the results of such seminal reviews with an even larger and wide-ranging sample of studies, in particular by focusing on the potentialities and limitations of the available methodologies in the field of psychometric network analysis.

Research question

In line with the application to other mental disorders, various research goals can be identified among the existing literature about network approaches to EDs, namely:

1. validation of the transdiagnostic model of eating disorders by comparing network characteristics across ED diagnoses [43,46,50,61,65,80,81];
2. estimation of the symptom network of EDs and identification of the core symptoms [32,45–47,74,85];
3. identification and interaction with nonspecific ED symptoms (i.e., the external field) like general psychiatric symptoms, personality traits and other clinical variables [68,80,81], embodiment dimensions [37], childhood maltreatment [60,65,67,73], mentalizing and empathy [64], vulnerability factors [84], suicidal thoughts and behaviors [78], perfectionism and interoceptive sensibility [62], affective and metacognitive symptoms [31,86], interoceptive awareness [34], sleep disturbance [72], well-being domains (49), inflexible and biased social interpretations, socioemotional functioning [33];
4. assessment of psychiatric comorbidities such as depression and anxiety [33,44,53,56,75,79], posttraumatic stress disorder [60,82], social anxiety disorder [76,99], obsessive- compulsive disorder [49,55,63,83], trait anxiety disorder [48], autism spectrum disorder [54], borderline personality disorder [41], and alcohol misuse [40];
5. comparison of estimated network structures among clinical and nonclinical [82], ethnic minority women [70], men and women [71], across developmental stages [35,38,77], and across different duration of illness [39];
6. characterization of the dynamic structure of systems and evaluation of intraindividual networks [57–59];
7. assessment of treatment outcome [36,44,51,52,66,69,79].

Collection of psychometric data

The accomplishment of the above research goals relies on the successful collection of datasets having specific peculiarities, since this will determine the possibility of estimating certain types of networks. The most typical starting point for this kind of analysis is clearly the selection of appropriate psychometric assessment tools, mainly self-report questionnaires and structured clinical interviews [5]. Depending on the sample size and the sampling frequency, three types of data environments can be identified among the current practice of network approaches to psychopathology, namely cross-sectional data, time-series data, and panel or longitudinal data.

Cross-sectional data has been the first type of data used in this field and is definitely the most mentioned across the existing literature (e.g., it was used in 48 papers out of 57 in our sample). It is particularly suitable for the estimation of group-level networks, since it provides variable measures taken at a single time point in a large sample. Importantly, the associations between variables are built upon differences among individuals and for such a reason a lot of caution should be taken when inferences about single patients are made, since the very strict conditions under which a structure of intraindividual variation can be deduced from the analogous structure of interindividual variation are seldom met in psychological processes [100,101]. In a cross-sectional dataset, rows can be reasonably assumed to be independent, therefore the corresponding PMRF can be directly estimated from it.

Time-series and panel data have been introduced in the psychometric network modeling in order to address two main limitations of cross-sectional data: the lack of clear understanding of individual networks and the inability to capture the dynamic features of psychopathology [5]. Both data environments are characterized by datasets where variables are measured at multiple time points, with the difference that time-series data focuses on one single individual, whereas panel data consist of observations of multiple individuals. Given a time-series dataset, one can estimate two different structures: a directed temporal network of vector autoregressive coefficients where links describe associations between variables through time, and an undirected contemporaneous network where links describe instead the association between variables after the temporal effects have been removed. In case of panel data, a third structure can be estimated, namely a between-subject network, where links indicate the conditional associations between the long-term averages of the time series between people [18].

In line with other experimental studies, the applications to EDs mostly move from cross-sectional data. Nevertheless, few exceptions are worth mentioning. Firstly, Levinson and coworkers in three different papers [57–59] used panel data to estimate interindividual networks (temporal, contemporaneous, and between-subject), as well as intra-individual networks (temporal and contemporaneous) for some of the patients in the sample. Other relevant studies aimed at assessing the treatment efficacy by applying statistical techniques [34,36,38,44,51,52,66,79].

Data vary in terms of other features as well. Among the articles under review, 50 out of 57 described their sample as being composed of a great majority of female participants. After all, the fact that EDs are much more common in women than in men is broadly known and documented [102], with reasons usually attributed to social pressure [103], adolescent turbulence, poor body concept, and role confusion [104]. Just one study involved only male participants [47], while few other papers reported a more heterogeneous (mostly nonclinical) sample with male participants within the range of 40–60% [33,53,55,60,71,75,76].

Moreover, in 60% of the cases, participants are reported as clinical, either inpatients or outpatients. Among these, three studies involved users of the Recovery Record [105] smartphone application [38,39,71]. Exceptions consist in mixed samples involving nonclinical patients, such as school or college students, and three case studies based on datasets collected through the crowdsourcing marketplace Amazon Mechanical Turk, (MTurk; [47,55,60]).

Nearly all papers focus on the most common ED diagnosis, namely Anorexia Nervosa (AN) and Bulimia Nervosa (BN). However, some of them also present results concerning secondary EDs, in particular binge-eating disorder [52,85], and night eating disorders [32].

Various psychometric assessment questionnaires were used as tools for data collection. For the evaluation of ED specific symptoms, the most widely used tests were the Eating Disorder Inventory (EDI; [87,93,98], the Eating Disorder Examination Questionnaire (EDE-Q; [92]), and the Eating Pathology Symptom Inventory (EPSI; [90]). For the assessment of general psychological factors other tests were also used, for example the Symptom Check‐List 90 (SCL-90; [106,107]), and the Beck Depression Inventory (BDI-II; [108]). Note that, among the cited psychometric tests, the only one that has been designed to assess both ED specific symptoms as well as other general integrative psychological constructs is EDI.

Methods for network estimation and reconstruction

Once the data has been collected, the next fundamental point is determining the variables of interest, that is, the nodes of the network. Instead of considering the totality of the items included in the questionnaires, a common practice is that of reducing their number in an effort to produce more accurate results by avoiding redundant (i.e., collinear) variables. The final nodes do not generally comprise all the items of the questionnaires. Instead, they are chosen in either one of the following ways, namely by taking into account just some special item aggregates such as questionnaires’ subscales, by employing the goldbricker() function of the R package networktools [109], which compares correlations between variables and identifies the collinear ones, or by combining the latter with a further theoretically driven selection of items.

Cross-sectional networks

The types of networks that can be estimated depend on what kind of data is available. In case of cross-sectional data, the main solutions are association networks, concentration (or partial correlation) graphs, regularized partial correlation networks, and Bayesian networks, where the first three types are undirected, weighted and can all be estimated with the qgraph [110] R package, while the last one is direct, either weighted or unweighted, and can be obtained with the help of the bnlearn [111] R package.

Association networks are the most basic types of networks that can be estimated from cross-sectional data. Edges correspond to zero-order correlations between symptoms, indicating the probability of their co-occurrence. For example, the qgraph() R function with input parameter graph = “cor” will compute an association network by estimating zero-order correlations between each pair of variables through the Pearson coefficient r.

Consider a set of p variables X = (X₁,…,X_p), each described by n observation, that is, . Given paired data , the Pearson coefficient is defined as: where n is the sample size, and are two sample points indexed with k, and are the sample means of the variables X_j and X_j.

Association networks have two main limitations: first, they do not give any information about the direction of causal relationships, and second, they do not discern true relations from spurious ones and from those caused by the influence of other nodes [5].

Concentration networks solve the second of these limitations by estimating edges as partial correlations between symptoms after adjusting for the influence of all other nodes in the networks; only the edges whose value is above a fixed threshold are then kept. Formally, the partial correlation between two variables X and Y given a set of n controlling variables Z ={z₁,…,z_n} is written as Corr(X_i,X_j|Z) and is given by the correlation between the residuals e_X and e_Y resulting from the linear regression of X with Z and of Y with Z, respectively. A network where each edge corresponds to the partial correlation between the connected nodes can be estimated through the qgraph() function by setting the parameter graph = “concentration”.

When dealing with p-multivariate data all information needed to compute the partial correlation coefficients is encoded in the variance-covariance matrix Σ. In fact, once its inverse is defined (i.e., the so-called precision matrix K), one can directly apply the following relationship to recover the partial correlation coefficients: where k_ij denotes the element in row i and column j of the precision matrix K = ∑⁻¹ and X_−(i,j) denotes the set of variables without X_i and X_j. These coefficients can be graphically displayed in a weighted undirected network where each node corresponds to a variable and edges between them are given by the partial correlation coefficients. If the ij^th component of ∑⁻¹ is zero, then the variables X_i and X_j are conditionally independent, given the other variables, and no edge will be traced between them. This model is a type of PMRF and it is called Gaussian Graphical Model, shortly GGM [24]. Forbush et al. [45] gave an example of an ED symptom network estimated as an association graph and also proposed the corresponding concentration network in the supplementary material of the same paper.

When the number of variables to estimate is high, it has been suggested that a more appropriate model to use is the regularized partial correlation network [112], obtainable running the gqraph() R function with input parameter graph =“glasso”. The result is similar to a concentration graph in the fact that edges indicate partial correlation between nodes, however it has the relevant difference of including the implementation of an L1 regularization technique called graphical LASSO (least absolute shrinkage and selection operator; [113]) which allows for the shrinking of all small partial correlations to zero. This procedure returns a sparse network that parsimoniously accounts for the covariance among nodes, in the sense that only the edges that are most robust and most likely to reflect real associations are kept [5]. Formally, the graphical LASSO gives an estimation of the precision matrix K = ∑⁻¹ by solving the optimization problem of maximize the penalized log-likelihood over nonnegative definite matrices K, where S is the empirical covariance matrix of X, λ is a nonnegative tuning parameter and ||K||₁ denotes the -norm, that is, the sum of the absolute values of the elements of ∑⁻¹. Hence, the higher the λ value, the more K_ij will be set to zero.

Clearly, if λ is too low, then too many spurious edges risk being included (i.e., yielding a high number of false positives), whereas if λ is too high, then the risk is to remove relevant connections (false negatives). Hence, the λ parameter needs to be tuned. The best model (i.e., the most likely to maximize the number of “true” edges while minimizing the spurious ones) is then identified through the Extended Bayesian Information Criterion (EBIC; [114]) for multiple λ values and then choosing the model with lowest EBIC score. Let P be a subset of {1,…,p} and let υ = |P| be the cardinality of this subset, then the best λ is chosen to be the one that maximizes where L_Σ(X) is the log-likelihood L_Σ(X) = −log det K−trace(SK) [114,115].

It has been suggested by Williams and Rast [116] that the graphical LASSO gives an accurate representation of data only when the number of nodes vastly exceeds the number of cases; if not, a non-regularized network should be preferred. Nevertheless, almost all of the articles under review based on cross-sectional data employ the graphical LASSO to estimate the symptom network.

Notably, in Monteleone et al. [66] the network structure of the cross-sectional data corresponding to each time period of the analysis is estimated via a Mixed Graphical Model (MGM), an extension of GGM that allows the integration of variables following two or more different data distribution [117]. In the specific case of this study, MGM was chosen in favor of GLASSO to include the treatment group as a binary variable into the model and thus assess its effect with respect to the treatment as usual (TAU) control group.

Bayesian networks attempt to discern causality by representing data as directed acyclic graphs (DAGs) where arrows indicate the direction of predictions and, possibly, causality [7]. DAGs depict the joint probability distribution of the variables and can thus be decomposed into the conditional distribution of each node given its parent. Importantly, dependence relations should not be confused with temporal antecedence, which cannot be derived from cross-sectional data in any way. What restrains Bayesian networks from widespread application is the existence of strict assumptions about data that it is pretty difficult to find in psychological analysis settings according to clinical observations [5]. The first condition is that all relevant causal variables should be included in the system. Second, the causal Markov Condition [7] must be met. Third, the probability distributions of certain variables might not be unrestricted. And fourth, it might not be easy to choose the best model among all possible ones [7]. Moreover, one additional assumption is suggested by the definition itself of DAGs, namely that all loops of any length are prohibited. A Bayesian network can be estimated from multivariate data through the bnlearn R package [111].

In a paper that analyzes the relationship between EDs and childhood abuse, Rodgers et al. [73] followed this Bayesian approach in two steps: they first wrote down a “blacklist” of forbidden edges to limit the investigation to patterns of symptom relationships that made both conceptual and clinical sense; next, they estimated the DAG through the hill-climbing algorithm. This is an iterative machine-learning process that starts with an arbitrary network structure and tries to improve it by making incremental changes to the network (e.g., adding, removing, or reversing edges). At each step, the Bayesian Information Criterion (BIC) is computed, and the change is kept if and only if it results in a lower BIC. This process continues until no further improvements can be found and the network model that represents the best fit for the interactive structure of the ED psychopathology is returned.

Diverging from the other studies, Bronstein et al. [33] employed a combined procedure to test different hypotheses. In particular, they used the exploratory causal discovery algorithm Greedy Fast Causal Inference (GFCI; [118]) to investigate potential causal pathways involving ED symptoms, biased and inflexible interpretations, and socioemotional functioning. GFCI takes as input a dataset of continuous variables (e.g., psychometric data) and outputs a graphical model called Partial Ancestral Graph (PAG; [119]), which is a representation of a set of Bayesian Networks that cannot be distinguished by the algorithm. Notably, GFCI is characterized by the ability of detecting latent confounders (i.e., an unmeasured variable that casually influences two or more measured variables); this information is conveyed by different edge types in the generated PAG.

Joint estimation of cross-sectional networks

In many of the studies under review, multiple networks were estimated with the specific aim of comparing their structure in various populations. As it will be later explained in more details, most often this task is accomplished by first estimating each network separately and only later some pivotal test statistics are computed to highlight global and local topological differences.

However, when the observations in a dataset consist of several distinct classes, it is also possible to adopt a recently developed technique called Joint Graphical Lasso (JGL), which allows for jointly estimating multiple graphical models corresponding to distinct but related conditions [120]. In particular, the JGL fits GGMs on data with the same variables observed on different classes but differs in the estimation of uncoupled GGMs from independent samples in the fact that, besides the lasso penalty on density, the regularized optimization problem for the evaluation of the precision matrices of each class includes an additional penalty term that is specifically written to foster similarity between groups.

Suppose we are given K datasets Y⁽¹⁾,…,Y^(K),K≥2, where each Y^(k) is a n_k×p matrix consisting of n_k observations on a set of p features common to all K datasets. We assume that all the observations are independent and that, within each dataset, . Then one can define the empirical covariance matrix for Y^(k) as . Danaher et al. [120] proposed to estimate the precision matrices (∑⁽¹⁾)⁻¹,…,(∑^(K))⁻¹ by maximizing the penalized log-likelihood where θ⁽¹⁾,…,θ^(k) are assumed to be positive definite and P({θ}) denotes a convex penalty function chosen to encourage precision matrices to share certain characteristics (e.g., the locations or values of the nonzero elements or the sparsity).

Depending on the explicit definition of the penalty function, JGLs are classified as Fused Graphical Lasso (FGL) and Group Graphical Lasso (GGL). The former encourages shared edge values across classes, whereas the latter only encourages a similar pattern of sparsity across all precision matrices. Hence, the FGL results in a stronger form of similarity [120]. The penalty of the FGL has the form where λ₁ and λ₂ are nonnegative tuning parameters, the first controlling the`-penalties applied to each off-diagonal element of the K precision matrices, the second those applied to the differences between corresponding elements of each pair of precision matrices. Hence, large values of λ₁ will increase the sparsity of the precision matrices (just like in graphical LASSO), while large values of λ₂ will cause many elements to be identical across classes.

Both types of JGL have already been implemented in the R package EstimateGroupNetwork [121], which also include methods for the automatic tuning parameter selection. A final consideration about JGL is that its network estimations cannot behave worse than independent GGMs [120–122]. In fact, when the tuning procedure selects a value of the corresponding tuning parameter equal or very close to zero, independent GGMs are estimated via typical graphical lasso. Therefore, JGL cannot hide differences nor inflate similarities across groups.

The JGL has been applied in the EDs research as well. Schlegl et al. [77] used the FGL with k-fold cross-validation for parameter selection to estimate four different networks, one for each of the following groups: adolescents with AN, adults with AN, adolescents with BN, and adults with BN. Similarly, Smith et al. [78] used the FGL to estimate and compare distinct networks from samples corresponding to either of the following groups: outpatients without ED diagnosis, outpatients with a lifetime attempt of suicide, and people with a current ED diagnosis. Martini et al. [62] employed FGL to compare a sample of AN patients with a control group. Finally, [47] jointly estimated and compared the network structures of two nonclinical samples of men with and without core ED symptoms.

Longitudinal and personalized networks

Time-series data allow for the estimation of personalized networks of two different kinds. Temporal networks incorporate consecutive temporal effects among symptoms by representing arrowhead edges pointing from one node to the other (or to itself in case of self-loops) when the first predicts the second in the next window of measurement. Edges are also weighted according to the regression parameters [123,124]. Temporal networks are commonly estimated as lag-1 Vector-Autoregression (VAR) models [125], which consist of a set of regression equations on the given variables; these are all treated as endogenous, so they act as both outcome and predicted variables. The relations assessed through this method can also be interpreted in terms of Granger causality [126] by stating that, whenever an arrow from a time-varying symptom X to another time-varying symptom Y is found, then X Granger-causes Y, meaning that predictions of the value of Y based on its own past values and on the past values of X are better than predictions of Y based only on Y’s own past values. Clearly, Granger causality should not be erroneously understood as pure causality. Rather, Granger causality gives evidence of temporal prediction and thus it can be potentially indicative of causality in the sense that, although the existence of a causal relationship would imply the observation of a temporal prediction, the opposite is not true, since temporal links may also arise for other reasons. In addition, some temporal predictions can also be missed because of lack of statistical power or insufficient sized lag interval [124].

The residuals of the temporal VAR model are used to compute the so-called contemporaneous network, which can be estimated as a GGM model, with edges representing the partial correlation obtained after controlling for both temporal effects and all other variables in the same window of measurement [124]. Together, the modeling framework including the estimation of both temporal and contemporaneous networks from a given dataset is called graphical VAR or GVAR [127]. It can be computed with the help of the R package graphicalVAR [128], which allows for both regularized and unregularized estimations [123].

When time-series of multiple subjects are available, it is possible to gain more insight into the network structure at the group-level by applying the multilevel-VAR model. For a given population, the average network parameters are called “fixed effects”, whereas the person-specific deviations from these fixed effects are called “random effects”. Random effects can be used to estimate intraindividual networks (temporal and contemporaneous) and to investigate interindividual differences [129]. Fixed effects can be instead used to uncover information about average intraindividual effects. More generally, if a multivariate normal is assumed for all parameters, then estimating the GVAR model on longitudinal data allows for the decomposition of the variance into three different structures, namely temporal networks, contemporaneous networks and between-subjects networks [123], where the latter is a GGM that allows for the examination of between-mean relationships for all individuals of the dataset. Estimation methods for multilevel-VAR models have been implemented in the R package mlVAR [128], which in particular permits to choose among different estimation procedures, such as sequential univariate multi-level estimation, multivariate Bayesian estimation, and fixed effects estimation.

In the context of the studies about EDs, Levinson et al. [57] first conducted a pilot study in which they collected longitudinal data from N = 66 participants by asking them to complete an Ecological Momentary Assessment (EMA) survey [130,131] on ED cognitions and behaviors across one week. Using the graphicalVAR and mlVAR packages, they then estimated intraindividual networks to identify which symptoms maintain EDs within each individual as well as group-level networks, namely temporal, contemporaneous and between-subject networks. Later, they repeated an analogous study on a different dataset composed of longitudinal data of N = 1272 participants with the additional goal of comparing adolescents and adults network structures [58]. More recently, another study was conducted to exclusively estimate the individual networks of N = 34 participants with the aim of identifying and discussing a range of target symptoms for personalized ED treatment [59].

Approaches and tools for network description

The analytical phase that follows the estimation of the network structure from data is designated to the investigation and interpretation of specific characteristics exhibited by either single nodes or groups of nodes jointly. Although a first visual inspection can give some general clues, many numerical methods can be employed to gain deeper insights.

Centrality measures in GGMs.

Depending on the type of network estimated, different measures can be used to investigate the role of each symptom in the network. In the case of undirected weighted networks, Opsahl et al. [132] proposed a generalization to weighted networks (see Table 2) of the most common measures of node centrality that were originally designed by Freeman [133] for binary networks, namely: degree, strength, closeness, and betweenness centrality.

Download:

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

Table 2. Definition and interpretation of common centrality measures.

https://doi.org/10.1371/journal.pone.0276341.t002

However, all the measures above only consider weights in absolute value with the consequence that two nodes may have same centrality but opposing effects on the rest of the network. For example, an increase in Node A can cause an increase in Node B (positive influence) with the same strength that an increase in Node C causes a decrease in Node D (negative influence). In this case, Node A and C will have the same centrality index but an opposite effect. Moreover, a node with a similar number of strong positive and negative edges may have little to no overall network activation impact, that is, it might be highly central without being highly influential. Hence, a new centrality metric called expected influence (EI) has been introduced to consider both negative and positive edges (see Table 2, last row; [134]).

As argued by Bringmann et al. [135], betweenness and closeness centrality do not seem to be especially suitable as measures of node importance. Hence, results about these metrics should be interpreted with care. As an additional proof about this fact, many articles reported betweenness and closeness centrality as not satisfying the minimum stability results and did not include their estimation in the network description [31,36,46,64,74,79,82]. Others decided instead to take these measures into account but did not assess their stability [45,69].

Throughout the large number of studies reviewed, few symptoms appeared among the most central ones across heterogeneous samples and estimation techniques. Among these: shape and weight overvaluation, body dissatisfaction, drive for thinness, ineffectiveness (i.e., feeling of inadequacy, insecurity, worthlessness and having no control over one’s life), and lack of interoceptive awareness (i.e., ability to identify, access, understand, and respond properly to the patterns of internal signal). For a complete list refer to Table 3.

Download:

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

Table 3. Central symptoms in psychopathology networks.

https://doi.org/10.1371/journal.pone.0276341.t003

Diverging from the other studies, 3 papers also assessed the importance of nodes using key players analysis. Specifically, they identified the nodes that, when removed, would result in a maximally disconnected residual network. In other words, a treatment targeting these key nodes is expected to slow the cascade of symptoms through the ED network. Analyzing the symptom network of a sample of participants with mixed ED diagnoses, Forbush et al. [45] identified its key players to be: people encouraged me to eat more, need to exercise nearly every day, and try to avoid foods with high calorie content. Perko et al. [71] employed this metric to assess sex differences in ED symptoms, but they found that the key players were, in both cases, items related restricting dieting and binge eating. More recently, Liebman et al. [60] explored the associations between posttraumatic stress disorder and ED symptom in presence of at least one experience of childhood abuse and found that the key players of the network were: purging, negative alterations in cognitions and mood, and hyperarousal.

Understanding comorbidities between EDs and other psychopathologies.

With the specific aim of identifying bridge symptoms, four network statistics have been developed and implemented in the R package networktools; importantly, since they are not specific to the type of network estimated, they can be readily applied to intraindividual networks, group-level networks, and other networks different from the psychopathology ones [138]. They are defined as follows:

• Bridge strength (BS), that is, the sum of the absolute value of every edge which connects a given symptom to symptoms belonging to other disorders. Bridge in-strength and bridge out-strength can be analogously defined in directed networks by considering only the subset of edges that are, respectively, directed toward the node or issued from a node.
• Bridge expected influence (BEI), which is defined just like the bridge strength but without taking the absolute value. In directed networks, only edges issuing from a node are summed.
• Bridge Closeness (BC), that is, the average distance from a given node to all nodes outside of its own disorder.
• Bridge betweenness (BB), that is, the number of times a given node lies on the shortest path between any two nodes belonging to two distinct disorders (including the one it belongs to).

Refer to Table 4 for the list of the bridge symptoms between EDs and other psychopathologies that have been assessed through the metrics defined above in some of the papers under review.

Download:

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

Table 4. Bridge symptoms between eating disorders and other psychopathologies.

https://doi.org/10.1371/journal.pone.0276341.t004

Assessing the role of the external field in the development and maintenance of Eds.

Interactions between ED specific symptoms and various elements of the external field have also been investigated. Few studies used the bridge centrality measures to accomplish this task. Monteleone et al. [67,137] chose instead to adopt a different approach to explore the psychological pathways through which childhood maltreatment (CM) experiences promote the development of ED core symptoms. Namely, they first selected few variables from items and scores of different psychometric questionnaires in order to build symptom networks for each ED diagnosis, then the shortest path between any CM and ED node was computed using Dijkstra’s algorithm, and finally they used mediation analysis to confirm the mediation role of the symptoms included in the shortest pathways from CM to ED specific symptoms. All the other studies considered all variables as a single community and chose to determine the core symptoms using the centrality measures in their classical form with the specific aim of verifying whether EDs are mainly maintained by ED specific symptoms or rather by nonspecific ones. The results achieved throughout the papers under review are summarized in Table 5.

Download:

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

Table 5. Interaction between eating disorders and the external field.

https://doi.org/10.1371/journal.pone.0276341.t005

Network stability analysis

Network stability analysis has been conducted in most of the papers under review, especially in those published after 2018, when Epskamp and his colleagues Borsboom and Fried [24] proposed precise guidelines for this task. In particular, they suggested specific methods to assess the robustness of the model at three distinct levels: accuracy of the estimated edge weights, stability of the order of centrality indices, and difference between specific edge weights or centrality indices.

Common methods for network comparison

Many of the studies under review aimed at comparing network structures across different populations. A specific tool to accomplish this task, namely the Network Comparison Test (NCT; [17]) has been devised and implemented in the R package NetworkComparisonTest [165]. Compared to other statistical tests, the NCT overcomes the usual assumption of normality and possible improper null hypothesis that are unsuitable for the regularized parameters that results after GGM estimation with LASSO regularization, the most typical method employed in the network approach to psychopathology.

The NCT is a 2-tailed permutation test in which the difference between two groups is calculated repeatedly for randomly regrouped individuals. It consists of three steps: first, the network structure is estimated for both groups using the original data and the metric of interest is calculated; second, data is permuted iteratively to rearrange group memberships, networks are then re-estimated, and metrics are calculated based on permuted data to create a reference distribution; finally, the significance of the observed test statistic is evaluated by comparing it to the reference distribution. In particular, the p-value equals the proportion of test statistics that are at least as extreme as the observed test statistic. Thus, the null hypothesis that the two networks under comparison are the same can be rejected if the latter is larger than expected (i.e., p-value < 0.05).

As for the test statistics that can be used to compare networks, Van Borkulo et al. [165] proposed three metrics that represent both global and local differences, namely invariance of network structure and global strength for the former case, and invariance of edge strength for the latter (see Table 6).

Download:

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

Table 6. Network comparison.

https://doi.org/10.1371/journal.pone.0276341.t006

The above test statistics have already been used in several studies about EDs. Significant results concerning the invariant network structure have been found in various comparisons, in particular: clinical versus nonclinical subsamples of networks assessing comorbidity between EDs and different features of social anxiety disorder [99]; admission against discharge network [36]; adolescents versus adults with AN and BN, with the exception of the comparison between adolescents with BN and adults with BN [77].

Moreover, significant results have been obtained when computing the invariant global strength for many pairs of networks, among those: groups of individuals with low versus high levels of overvaluation of shape and weight, with the latter resulting in higher connectivity [43]; clinical versus nonclinical samples, with a higher density in the former [82]; groups of individuals split based on the median value of the EDE-Q global scores at admission and discharge, with denser networks at admission predicting less change in ED symptomatology during treatment [79]; pre- to post treatment networks, with increased connectivity in the latter [52]; admission against discharge network, with decreased connectivity in the latter [36]; adolescents with AN versus adolescents with BN, adolescents with AN and adults with BN, both cases with higher global strength in the AN sample [77]; men with core ED symptoms versus men without them [47]; men versus women [71]; and across developmental stages [38].

Finally, having found a significant variation in the network structures, Calugi et al. [36] also tested the change in weight of links from admission to discharge. He identified few connections that were stronger at baseline than at discharge, namely feelings of fatness and desiring weight loss, BMI and vomiting to control shape or weight, and others whose relationship grew at discharge, namely food preoccupation and desiring weight loss, fear of losing control overeating and vomiting to control shape or weight, feelings of fatness and dissatisfaction with weight and shape. Schlegl et al. [77] reported instead the percentage of edges that were significantly different in each pair of networks which resulted to have significant invariant network structure statistics. The values found ranged from 2.56% for the adolescents with AN versus adults with AN comparison to 10% for the adolescents with AN versus adults with BN comparison.

Remarkably, many studies reported no differences in network structure nor in global strength with regards to different ED diagnoses [42,50,61], age [34,35,75], and sex [75,76].

One study assessing the network differences from admission to discharge, although not finding any significant changes in the global strength, reported a significant effect of time on symptom severity, indicating decreases in ED, depression, and anxiety symptoms, with medium to large effect sizes [79]. These results were assessed through repeated measures multivariate analysis of variance (RM MANOVA), which is a statistical technique to determine the degree to which multiple dependent variables (e.g., total scores of psychometric assessment tests) vary across time points.