The Gaussian Graphical Model in Cross-Sectional and Time-Series Data

We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse modeling of covariance structures, and may highlight potential causal relationships between observed variables. We describe the utility in three kinds of psychological data sets: data sets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered data sets (e.g., n = 1 time series), and a mixture of the 2 (e.g., n > 1 time series). In time-series analysis, the GGM can be used to model the residual structure of a vector-autoregression analysis (VAR), also termed graphical VAR. Two network models can then be obtained: a temporal network and a contemporaneous network. When analyzing data from multiple subjects, a GGM can also be formed on the covariance structure of stationary means-the between-subjects network. We discuss the interpretation of these models and propose estimation methods to obtain these networks, which we implement in the R packages graphicalVAR and mlVAR. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials.

Personalized Network Modeling in Psychopathology: The Importance of Contemporaneous and Temporal Connections

Recent literature has introduced (a) the network perspective to psychology and (b) collection of time series data to capture symptom fluctuations and other time varying factors in daily life. Combining these trends allows for the estimation of intraindividual network structures. We argue that these networks can be directly applied in clinical research and practice as hypothesis generating structures. Two networks can be computed: a temporal network, in which one investigates if symptoms (or other relevant variables) predict one another over time, and a contemporaneous network, in which one investigates if symptoms predict one another in the same window of measurement. The contemporaneous network is a partial correlation network, which is emerging in the analysis of cross-sectional data but is not yet utilized in the analysis of time series data. We explain the importance of partial correlation networks and exemplify the network structures on time series data of a psychiatric patient.

A tutorial on regularized partial correlation networks

Recent years have seen an emergence of network modeling applied to moods, attitudes, and problems in the realm of psychology. In this framework, psychological variables are understood to directly affect each other rather than being caused by an unobserved latent entity. In this tutorial, we introduce the reader to estimating the most popular network model for psychological data: the partial correlation network. We describe how regularization techniques can be used to efficiently estimate a parsimonious and interpretable network structure in psychological data. We show how to perform these analyses in R and demonstrate the method in an empirical example on posttraumatic stress disorder data. In addition, we discuss the effect of the hyperparameter that needs to be manually set by the researcher, how to handle non-normal data, how to determine the required sample size for a network analysis, and provide a checklist with potential solutions for problems that can arise when estimating regularized partial correlation networks. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

False alarm? A comprehensive reanalysis of "Evidence that psychopathology symptom networks have limited replicability" by Forbes, Wright, Markon, and Krueger (2017)

Forbes, Wright, Markon, and Krueger (2017) stated that "psychopathology networks have limited replicability" (p. 1011) and that "popular network analysis methods produce unreliable results" (p. 1011). These conclusions are based on an assessment of the replicability of four different network models for symptoms of major depression and generalized anxiety across two samples; in addition, Forbes et al. analyzed the stability of the network models within the samples using split-halves. Our reanalysis of the same data with the same methods led to results directly opposed to theirs: All network models replicated very well across the two data sets and across the split-halves. We trace the differences between Forbes et al.'s results and our own to the fact that they did not appear to accurately implement all network models and used debatable metrics to assess replicability. In particular, they deviated from existing estimation routines for relative importance networks, did not acknowledge the fact that the skip structure used in the interviews strongly distorted correlations between symptoms, and incorrectly assumed that network structures and metrics should be the same not only across the different samples but also across the different network models used. In addition to a comprehensive reanalysis of the data, we end with a discussion of best practices concerning future research into the replicability of psychometric networks. (PsycINFO Database Record

Bayesian inference for psychology. Part II: Example applications with JASP

Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t-test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP ( http://www.jasp-stats.org ), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder's BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.

Estimating psychological networks and their accuracy: A tutorial paper

The usage of psychological networks that conceptualize behavior as a complex interplay of psychological and other components has gained increasing popularity in various research fields. While prior publications have tackled the topics of estimating and interpreting such networks, little work has been conducted to check how accurate (i.e., prone to sampling variation) networks are estimated, and how stable (i.e., interpretation remains similar with less observations) inferences from the network structure (such as centrality indices) are. In this tutorial paper, we aim to introduce the reader to this field and tackle the problem of accuracy under sampling variation. We first introduce the current state-of-the-art of network estimation. Second, we provide a rationale why researchers should investigate the accuracy of psychological networks. Third, we describe how bootstrap routines can be used to (A) assess the accuracy of estimated network connections, (B) investigate the stability of centrality indices, and (C) test whether network connections and centrality estimates for different variables differ from each other. We introduce two novel statistical methods: for (B) the correlation stability coefficient, and for (C) the bootstrapped difference test for edge-weights and centrality indices. We conducted and present simulation studies to assess the performance of both methods. Finally, we developed the free R-package bootnet that allows for estimating psychological networks in a generalized framework in addition to the proposed bootstrap methods. We showcase bootnet in a tutorial, accompanied by R syntax, in which we analyze a dataset of 359 women with posttraumatic stress disorder available online.

Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications

Bayesian parameter estimation and Bayesian hypothesis testing present attractive alternatives to classical inference using confidence intervals and p values. In part I of this series we outline ten prominent advantages of the Bayesian approach. Many of these advantages translate to concrete opportunities for pragmatic researchers. For instance, Bayesian hypothesis testing allows researchers to quantify evidence and monitor its progression as data come in, without needing to know the intention with which the data were collected. We end by countering several objections to Bayesian hypothesis testing. Part II of this series discusses JASP, a free and open source software program that makes it easy to conduct Bayesian estimation and testing for a range of popular statistical scenarios (Wagenmakers et al. this issue).

An Introduction to Network Psychometrics: Relating Ising Network Models to Item Response Theory Models

In recent years, network models have been proposed as an alternative representation of psychometric constructs such as depression. In such models, the covariance between observables (e.g., symptoms like depressed mood, feelings of worthlessness, and guilt) is explained in terms of a pattern of causal interactions between these observables, which contrasts with classical interpretations in which the observables are conceptualized as the effects of a reflective latent variable. However, few investigations have been directed at the question how these different models relate to each other. To shed light on this issue, the current paper explores the relation between one of the most important network models-the Ising model from physics-and one of the most important latent variable models-the Item Response Theory (IRT) model from psychometrics. The Ising model describes the interaction between states of particles that are connected in a network, whereas the IRT model describes the probability distribution associated with item responses in a psychometric test as a function of a latent variable. Despite the divergent backgrounds of the models, we show a broad equivalence between them and also illustrate several opportunities that arise from this connection.

Generalized Network Psychometrics: Combining Network and Latent Variable Models

We introduce the network model as a formal psychometric model, conceptualizing the covariance between psychometric indicators as resulting from pairwise interactions between observable variables in a network structure. This contrasts with standard psychometric models, in which the covariance between test items arises from the influence of one or more common latent variables. Here, we present two generalizations of the network model that encompass latent variable structures, establishing network modeling as parts of the more general framework of structural equation modeling (SEM). In the first generalization, we model the covariance structure of latent variables as a network. We term this framework latent network modeling (LNM) and show that, with LNM, a unique structure of conditional independence relationships between latent variables can be obtained in an explorative manner. In the second generalization, the residual variance-covariance structure of indicators is modeled as a network. We term this generalization residual network modeling (RNM) and show that, within this framework, identifiable models can be obtained in which local independence is structurally violated. These generalizations allow for a general modeling framework that can be used to fit, and compare, SEM models, network models, and the RNM and LNM generalizations. This methodology has been implemented in the free-to-use software package lvnet, which contains confirmatory model testing as well as two exploratory search algorithms: stepwise search algorithms for low-dimensional datasets and penalized maximum likelihood estimation for larger datasets. We show in simulation studies that these search algorithms perform adequately in identifying the structure of the relevant residual or latent networks. We further demonstrate the utility of these generalizations in an empirical example on a personality inventory dataset.

What is the p-factor of psychopathology? Some risks of general factor modeling

Recent research has suggested that a range of psychological disorders may stem from a single underlying common factor, which has been dubbed the p-factor. This finding may spur a line of research in psychopathology very similar to the history of factor modeling in intelligence and, more recently, personality research, in which similar general factors have been proposed. We point out some of the risks of modeling and interpreting general factors, derived from the fields of intelligence and personality research. We argue that: (a) factor-analytic resolution, i.e., convergence of the literature on a particular factor structure, should not be expected in the presence of multiple highly similar models; and (b) the true underlying model may not be a factor model at all, because alternative explanations can account for the correlational structure of psychopathology.

Estimating psychopathological networks: Be careful what you wish for

Network models, in which psychopathological disorders are conceptualized as a complex interplay of psychological and biological components, have become increasingly popular in the recent psychopathological literature (Borsboom, et. al., 2011). These network models often contain significant numbers of unknown parameters, yet the sample sizes available in psychological research are limited. As such, general assumptions about the true network are introduced to reduce the number of free parameters. Incorporating these assumptions, however, means that the resulting network will lead to reflect the particular structure assumed by the estimation method-a crucial and often ignored aspect of psychopathological networks. For example, observing a sparse structure and simultaneously assuming a sparse structure does not imply that the true model is, in fact, sparse. To illustrate this point, we discuss recent literature and show the effect of the assumption of sparsity in three simulation studies.

Exploratory graph analysis: A new approach for estimating the number of dimensions in psychological research

The estimation of the correct number of dimensions is a long-standing problem in psychometrics. Several methods have been proposed, such as parallel analysis (PA), Kaiser-Guttman's eigenvalue-greater-than-one rule, multiple average partial procedure (MAP), the maximum-likelihood approaches that use fit indexes as BIC and EBIC and the less used and studied approach called very simple structure (VSS). In the present paper a new approach to estimate the number of dimensions will be introduced and compared via simulation to the traditional techniques pointed above. The approach proposed in the current paper is called exploratory graph analysis (EGA), since it is based on the graphical lasso with the regularization parameter specified using EBIC. The number of dimensions is verified using the walktrap, a random walk algorithm used to identify communities in networks. In total, 32,000 data sets were simulated to fit known factor structures, with the data sets varying across different criteria: number of factors (2 and 4), number of items (5 and 10), sample size (100, 500, 1000 and 5000) and correlation between factors (orthogonal, .20, .50 and .70), resulting in 64 different conditions. For each condition, 500 data sets were simulated using lavaan. The result shows that the EGA performs comparable to parallel analysis, EBIC, eBIC and to Kaiser-Guttman rule in a number of situations, especially when the number of factors was two. However, EGA was the only technique able to correctly estimate the number of dimensions in the four-factor structure when the correlation between factors were .7, showing an accuracy of 100% for a sample size of 5,000 observations. Finally, the EGA was used to estimate the number of factors in a real dataset, in order to compare its performance with the other six techniques tested in the simulation study.

Mapping the manuals of madness: Comparing the ICD-10 and DSM-IV-TR using a network approach

The International Classification of Diseases and Related Health Problems (ICD) and the Diagnostic and Statistical Manual of Mental Disorders (DSM) represent dominant approaches to diagnosis of mental disorders. However, it is unclear how these alternative systems relate to each other when taking into account the symptoms that make up the disorders. This study uses a network approach to investigate the overlap in structure between diagnostic networks pertaining to ICD-10 and DSM-IV-TR. Networks are constructed by representing individual symptoms as nodes, and connecting nodes whenever the corresponding symptoms feature as diagnostic criteria for the same mental disorder. Results indicate that, relative to the DSM-IV-TR network, the ICD-10 network contains (a) more nodes, (b) lower level of clustering, and (c) a higher level of connectivity. Both networks show features of a small world, and have similar (of "the same") high centrality nodes. Comparison to empirical data indicates that the DSM-IV-TR network structure follows comorbidity rates more closely than the ICD-10 network structure. We conclude that, despite their apparent likeness, ICD-10 and DSM-IV-TR harbour important structural differences, and that both may be improved by matching diagnostic categories more closely to empirically determined network structures. Copyright © 2016 John Wiley & Sons, Ltd.

What are 'good' depression symptoms? Comparing the centrality of DSM and non-DSM symptoms of depression in a network analysis

BACKGROUND

The symptoms for Major Depression (MD) defined in the DSM-5 differ markedly from symptoms assessed in common rating scales, and the empirical question about core depression symptoms is unresolved. Here we conceptualize depression as a complex dynamic system of interacting symptoms to examine what symptoms are most central to driving depressive processes.

METHODS

We constructed a network of 28 depression symptoms assessed via the Inventory of Depressive Symptomatology (IDS-30) in 3,463 depressed outpatients from the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) study. We estimated the centrality of all IDS-30 symptoms, and compared the centrality of DSM and non-DSM symptoms; centrality reflects the connectedness of each symptom with all other symptoms.

RESULTS

A network with 28 intertwined symptoms emerged, and symptoms differed substantially in their centrality values. Both DSM symptoms (e.g., sad mood) and non-DSM symptoms (e.g., anxiety) were among the most central symptoms, and DSM criteria were not more central than non-DSM symptoms.

LIMITATIONS

Many subjects enrolled in STAR*D reported comorbid medical and psychiatric conditions which may have affected symptom presentation.

CONCLUSION

The network perspective neither supports the standard psychometric notion that depression symptoms are equivalent indicators of MD, nor the common assumption that DSM symptoms of depression are of higher clinical relevance than non-DSM depression symptoms. The findings suggest the value of research focusing on especially central symptoms to increase the accuracy of predicting outcomes such as the course of illness, probability of relapse, and treatment response.

Exploring the underlying structure of mental disorders: cross-diagnostic differences and similarities from a network perspective using both a top-down and a bottom-up approach

BACKGROUND

It has been suggested that the structure of psychopathology is best described as a complex network of components that interact in dynamic ways. The goal of the present paper was to examine the concept of psychopathology from a network perspective, combining complementary top-down and bottom-up approaches using momentary assessment techniques.

METHOD

A pooled Experience Sampling Method (ESM) dataset of three groups (individuals with a diagnosis of depression, psychotic disorder or no diagnosis) was used (pooled N = 599). The top-down approach explored the network structure of mental states across different diagnostic categories. For this purpose, networks of five momentary mental states ('cheerful', 'content', 'down', 'insecure' and 'suspicious') were compared between the three groups. The complementary bottom-up approach used principal component analysis to explore whether empirically derived network structures yield meaningful higher order clusters.

RESULTS

Individuals with a clinical diagnosis had more strongly connected moment-to-moment network structures, especially the depressed group. This group also showed more interconnections specifically between positive and negative mental states than the psychotic group. In the bottom-up approach, all possible connections between mental states were clustered into seven main components that together captured the main characteristics of the network dynamics.

CONCLUSIONS

Our combination of (i) comparing network structure of mental states across three diagnostically different groups and (ii) searching for trans-diagnostic network components across all pooled individuals showed that these two approaches yield different, complementary perspectives in the field of psychopathology. The network paradigm therefore may be useful to map transdiagnostic processes.

Transdiagnostic Networks: Commentary on Nolen-Hoeksema and Watkins (2011)

Nolen-Hoeksema and Watkins (2011, this issue) propose a useful model for thinking about transdiagnostic processes involved in mental disorders. Here, we argue that their model is naturally compatible with a network account of mental disorders, in which disorders are viewed as sets of mutually reinforcing symptoms. We show that network models are typically transdiagnostic in nature, because different disorders often share symptoms. We illustrate this by constructing a network for generalized anxiety and major depression. In addition, we show that even a simple network structure naturally accounts for the phenomena of multifinality and divergent trajectories that Nolen-Hoeksema and Watkins identify as crucial in thinking about transdiagnostic phenomena.

From loss to loneliness: The relationship between bereavement and depressive symptoms

Spousal bereavement can cause a rise in depressive symptoms. This study empirically evaluates 2 competing explanations concerning how this causal effect is brought about: (a) a traditional latent variable explanation, in which loss triggers depression which then leads to symptoms; and (b) a novel network explanation, in which bereavement directly affects particular depression symptoms which then activate other symptoms. We used data from the Changing Lives of Older Couples (CLOC) study and compared depressive symptomatology, assessed via the 11-item Center for Epidemiologic Studies Depression Scale (CES-D), among those who lost their partner (N = 241) with a still-married control group (N = 274). We modeled the effect of partner loss on depressive symptoms either as an indirect effect through a latent variable, or as a direct effect in a network constructed through a causal search algorithm. Compared to the control group, widow(er)s' scores were significantly higher for symptoms of loneliness, sadness, depressed mood, and appetite loss, and significantly lower for happiness and enjoyed life. The effect of partner loss on these symptoms was not mediated by a latent variable. The network model indicated that bereavement mainly affected loneliness, which in turn activated other depressive symptoms. The direct effects of spousal loss on particular symptoms are inconsistent with the predictions of latent variable models, but can be explained from a network perspective. The findings support a growing body of literature showing that specific adverse life events differentially affect depressive symptomatology, and suggest that future studies should examine interventions that directly target such symptoms.

The small world of psychopathology

BACKGROUND

Mental disorders are highly comorbid: people having one disorder are likely to have another as well. We explain empirical comorbidity patterns based on a network model of psychiatric symptoms, derived from an analysis of symptom overlap in the Diagnostic and Statistical Manual of Mental Disorders-IV (DSM-IV).

PRINCIPAL FINDINGS

We show that a) half of the symptoms in the DSM-IV network are connected, b) the architecture of these connections conforms to a small world structure, featuring a high degree of clustering but a short average path length, and c) distances between disorders in this structure predict empirical comorbidity rates. Network simulations of Major Depressive Episode and Generalized Anxiety Disorder show that the model faithfully reproduces empirical population statistics for these disorders.

CONCLUSIONS

In the network model, mental disorders are inherently complex. This explains the limited successes of genetic, neuroscientific, and etiological approaches to unravel their causes. We outline a psychosystems approach to investigate the structure and dynamics of mental disorders.