PSYCHOMETRIC NETWORK ANALYSIS OF EATING (PDF)

PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 1 Network-Based Methods for Psychometric Data of Eating Disorders: A Systematic Review Clara Punzi1, Manuela Petti2,3* and Paolo Tieri1,4 1 Data Science Program, Sapienza University of Rome, Via Ariosto 25, 00185 Rome, Italy 2 DIAG Department of Computer, Control and Management Engineering, Sapienza University of Rome, Via Ariosto 25, 00185 Rome, Italy 3 FSL Fondazione Santa Lucia IRCCS, Via Ardeatina 306/354, 00179 Rome, Italy 4 CNR National Research Council, IAC Institute for Applied Computing, Via dei Taurini 19, 00185 Rome, Italy * to whom correspondence should be addressed Author Note We have no conflicts of interest to disclose. Correspondence concerning this article should be addressed to Manuela Petti, University of Rome “La Sapienza”, DIAG Dept. of Computer, Control, and Management Engineering, Via Ariosto 25, Rome 00185, Italy. Email: [email protected] . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 2 Abstract Network science represents a powerful and increasingly promising method for studying complex real-world problems. In the last decade, it has been applied to psychometric data in the attempt to explain psychopathologies as complex systems of causally interconnected symptoms. With this work, we aimed to review a large sample of network-based studies that exploit psychometric data related to eating disorders (ED) trying to highlight important aspects such as core symptoms, influences of external factors, comorbidities, and changes in network structure and connectivity across both time and subpopulations. A particular focus is here given to the potentialities and limitations of the available methodologies used in the field. At the same time, we also give a review of the statistical software packages currently used to carry out each phase of the network estimation and analysis workflow. Although many theoretical results, especially those concerning the ED core symptoms, have already been confirmed by multiple studies, their supporting function in clinical treatment still needs to be thoroughly assessed. Keywords: network science, psychometric data, eating disorders, symptoms network, graph theory . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 3 Introduction In the last century, the paradigm that best got ahead in Western medicine has been the “disease model” (Borsboom & Cramer, 2013), according to which all symptoms a person exhibits result from a latent entity that should therefore be targeted to an effective treatment to obtain, as a consequence, the lessening of all the deriving symptoms (Jones et al., 2017; McNally, 2021). Unfortunately, in contrast with general medicine, in most mental disorders the identification of common pathogenic pathways has proven elusive (Borsboom, 2017; Borsboom & Cramer, 2013; McNally, 2016, 2021), given that they cannot be diagnosed independently of their symptoms (Borsboom & Cramer, 2013). Therefore, the need of conceptualizing in an alternative way the relation between symptoms and disorders arose in the twenty-first century and led to the delineation of the network theory of psychopathology, an innovative approach that inspired an exponentially increasing number of empirical publications in the past two decades, especially after the seminal article by Borsboom and Cramer (2013) was published. Differently from the disease model, in the network model, symptoms are conceptualized as mutually interacting and reciprocally reinforcing elements of a complex network, i.e., causally active components of the mental disorder instead of passive receptors of its causal influence (see Figure 1). In the present work, we aim to describe the current state-of-the-art of the network conceptualization of a specific psychopathology, namely eating disorders (EDs). These are severe psychiatric syndromes defined by abnormal eating behaviors that negatively affect a person's physical or mental health (American Psychiatric Association, 2013). They are believed to result from and be sustained by sociocultural, psychological, and biological factors. Anorexia nervosa (AN), bulimia nervosa (BN), and binge eating disorder (BED) are the primary diagnoses associated with ED. . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 4 a) b) Figure 1. Comparison between Factor and Network Model. Schematic representation of factor model (a) and network model (b) of eating disorders (simplified). While in the first case symptoms (white rectangles) are considered manifestations of some common underlying factor (e.g., the eating disorder psychopathology [cyan ellipse]), according to the network model symptoms are conceptualized as mutually interacting and reciprocally reinforcing elements of a complex network where ED-specific symptoms (white rectangles in the red dashed box) mutually influence non-specific ones (yellow rectangles), such as external events (orange dashed box) or comorbidities (cyan ellipses in the blue dashed box). Hence, symptoms are seen as causally active components of the mental disorder instead of passive receptors of its causal influence. . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 5 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 (Borsboom, 2017). 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 (Bollobás, 1998). 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. Barabási 2004; 2011; 2016; Tieri et al., 2019). 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 . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 6 network (Borsboom, 2017). 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 (Borsboom, 2017; Cramer et al., 2010; McNally, 2016, 2021). 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 (Cramer, 2013). 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 (Borsboom, 2017). As proven by Cramer (2013) 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 (Borsboom, 2017). Following these observations, Borsboom (2017) 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 (Borsboom, 2017). 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 . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 7 methodology used in network approaches to multivariate psychometric data (Borsboom & Cramer, 2013; Borsboom et al., 2021; Christensen et al., 2018; Cramer et al., 2010; Forbes et al., 2017). The complete workflow (Figure 2) 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 (Borsboom et al., 2021). 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 (McNally, 2021). 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 (McNally, 2021), 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; Letina et al., 2018). . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 8 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 (Borsboom et al., 2018; Christensen & Golino, 2021; Epskamp, Borsboom, et al., 2018; Fried & Cramer, 2017; Fried et al., 2021). 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 (Fried & Cramer, 2017). 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 (Borsboom et al., 2021). The aim of this study is to review the existing literature on psychometric network analysis of EDs. To our knowledge, three other reviews on EDs have already been published (Levinson et al., 2018c; Monteleone & Cascino, 2021; Smith et al., 2018). We intend to update and broaden the results of such seminal reviews with a 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. Figure 2. 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. . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 9 Methods To ensure a standardized review procedure, the Preferred Reporting Items for Systematic reviews and Meta-analyses (PRISMA) 2020 statement (Page et al., 2021) was followed. The articles included in this study were extracted from those returned by the query run on PubMed in February 2022 with search keys (("eating disorder*"[Title/Abstract]) OR ("bulimia nervosa"[Title/Abstract]) OR ("anorexia nervosa"[Title/Abstract])) AND (network analys*[Title/Abstract]). The original collection of 89 papers was further narrowed down to a number of 54 by considering the following exclusion criteria: (1) studies not based on psychometric data, (2) studies with aims different from the investigation of eating disorders, and (3) review articles. The final subset of 56 papers was obtained by adding two more articles cited as references in the selected publications. The list of such papers is provided in the supplemental materials. The PRISMA flow chart corresponding to the present methodology is shown in Figure 3. Figure 3. PRISMA flow chart for selection and filtering of studies. . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 10 Results In the following, we analyzed a large sample of network-based studies that exploit psychometric data related to ED. Specifically, we first introduce each step of the (general) psychometric network analysis workflow and then describe and compare the results reported in the articles under review. 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: A. validation of the transdiagnostic model of eating disorders by comparing network characteristics across ED diagnoses (DuBois et al., 2017; Forrest et al., 2018; Goldschmidt et al., 2018; Mares et al., 2021; Monteleone, Tzischinsky, et al., 2022; Solmi et al., 2018; Solmi et al., 2019); B. estimation of the symptom network of EDs and identification of the core symptoms (Beauchamp et al., 2021; Forbush et al., 2016; Forrest et al., 2018; Forrest, Perkins, et al., 2019; Rodgers et al., 2018; Wang et al., 2019); C. identification and interaction with nonspecific ED symptoms (i.e., the external field) like general psychiatric symptoms, personality traits and other clinical variables (Monteleone, Mereu, et al., 2019; Solmi et al., 2018; Solmi et al., 2019), embodiment dimensions (Cascino et al., 2019), childhood maltreatment (Liebman et al., 2021; Monteleone, Cascino, et al., 2019; Monteleone, Tzischinsky, et al., 2022; Rodgers et al., 2019), mentalizing and empathy (Monteleone et al., 2020), vulnerability factors (Vervaet et al., 2021), suicidal thoughts and behaviors (Smith et al., 2020), perfectionism and interoceptive sensibility (Martini et al., 2021), affective and metacognitive symptoms (Aloi et al., 2021; Wong et al., 2021), interoceptive awareness (Brown et al., 2020), sleep disturbance (Ralph-Nearman et al., 2021), well-being domains (de Vos et al., 2021), inflexible and biased social interpretations, socioemotional functioning (Bronstein et al., 2022); D. assessment of psychiatric comorbidities such as depression and anxiety (Bronstein et al., 2022; Elliott et al., 2020; Kenny et al., 2021; Levinson et al., 2017; Sahlan, Williams, et al., . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 11 2021; Smith et al., 2019), posttraumatic stress disorder (Liebman et al., 2021; Vanzhula et al., 2019), social anxiety disorder (Levinson et al., 2018a; Sahlan, Keshishian, et al., 2021), obsessive- compulsive disorder (Giles et al., 2022; Kinkel-Ram et al., 2021; Meier et al., 2020; Vanzhula et al., 2021), trait anxiety disorder (Forrest, Sarfan, et al., 2019), autism spectrum disorder (Kerr-Gaffney et al., 2020), borderline personality disorder (De Paoli et al., 2020), and alcohol misuse (Cusack et al., 2021); E. comparison of estimated network structures among clinical and nonclinical (Vanzhula et al., 2019), ethnic minority women (Perez et al., 2021), men and women (Perko et al., 2019), across developmental stages (Calugi et al., 2020; Christian et al., 2020; Schlegl et al., 2021), and across different duration of illness (Christian et al., 2021); F. characterization of the dynamic structure of systems and evaluation of intraindividual networks (Levinson et al., 2021; Levinson et al., 2018b; Levinson et al., 2020); G. assessment of treatment outcome (Calugi et al., 2021; Elliott et al., 2020; Hagan et al., 2021; Hilbert et al., 2020; Olatunji et al., 2018; Smith et al., 2019). 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 (McNally, 2021). 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 56 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 . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 12 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 (Bos & Wanders, 2016; Molenaar, 2009). 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 (McNally, 2021). 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 (Borsboom et al., 2021). 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 (2021; 2018; 2020) 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 (Brown et al., 2020; Calugi et al., 2021; Christian et al., 2020; Elliott et al., 2020; Hagan et al., 2021; Hilbert et al., 2020; Smith et al., 2019). Data vary in terms of other features as well. Among the articles under review, 49 out of 56 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 . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 13 (Striegel-Moore et al., 2009), with reasons usually attributed to social pressure (Whiteman, 2016), adolescent turbulence, poor body concept, and role confusion (Hsu, 1989). Just one study involved only male participants (Forrest, Perkins, et al., 2019), while few other papers reported a more heterogeneous (mostly nonclinical) sample with male participants within the range of 40-60% (Bronstein et al., 2022; Kenny et al., 2021; Kinkel-Ram et al., 2021; Liebman et al., 2021; Perko et al., 2019; Sahlan, Keshishian, et al., 2021; Sahlan, Williams, et al., 2021). Moreover, in 60% of the cases, participants are reported as clinical, either inpatients or outpatients. Among these, three studies involved users of the Recovery Record1 smartphone application (Christian et al., 2020; 2021; Perko et al., 2019). 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; Forrest, Perkins, et al., 2019; Kinkel-Ram et al., 2021; Liebman et al., 2021). 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 (Hilbert et al., 2020; Wang et al., 2019), and night eating disorders (Beauchamp et al., 2021), 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; Garner et al., 1983; Garner, 1991; 2004), the Eating Disorder Examination Questionnaire (EDE-Q; Fairburn & Beglin, 1994), and the Eating Pathology Symptom Inventory (EPSI; Forbush et al. 2013). For the assessment of general psychological factors other tests were also used, for example the Symptom Check‐List 90 (SCL-90; (Derogatis & Cleary, 1977; Derogatis & Unger, 2010), and the Beck Depression Inventory (BDI-II; Beck et al., 1996). 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. 1 Recovery Record is an eating disorder management app used for either patient or clinicians (Tregarthen et al. 2015). . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 14 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 (Jones, 2018), 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 (Epskamp et al., 2012) R package, while the last one is direct, either weighted or unweighted, and can be obtained with the help of the bnlearn (Scutari, 2009) 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 , each described by n observation, that is, . Given paired data , the Pearson coefficient is defined as: . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint  PSYCHOMETRIC NETWORK ANALYSIS OF EATING DISORDERS 15 where n is the sample size, and are two sample points indexed with k, and are the sample means of the variables . 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 (McNally, 2021). 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 is written as and is given by the correlation between the residuals eX and eY 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: . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 16, 2022. ; https://doi.org/10.1101/2022.03.15.22272402 doi: medRxiv preprint