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.
IMPORTANCE: Major depressive disorder (MDD) is a heterogeneous condition in terms of symptoms, course, and underlying disease mechanisms. Current classifications do not adequately address this ...complexity. In novel network approaches to psychopathology, psychiatric disorders are conceptualized as complex dynamic systems of mutually interacting symptoms. This perspective implies that a more densely connected network of symptoms is indicative of a poorer prognosis, but, to date, no previous study has examined whether network structure is indeed associated with the longitudinal course of MDD. OBJECTIVE: To examine whether the baseline network structure of MDD symptoms is associated with the longitudinal course of MDD. DESIGN, SETTING, AND PARTICIPANTS: In this prospective study, in which remittent and persistent MDD was defined on the basis of a follow-up assessment after 2 years, 515 patients from the Netherlands Study of Depression and Anxiety with past-year MDD (established with the Composite International Diagnostic Interview) and at least moderate depressive symptoms (assessed with the Inventory of Depressive Symptomatology IDS) at baseline were studied. Baseline starting and ending dates were September 1, 2004, through February 28, 2007. Follow-up starting and ending dates were September 1, 2006, through February 28, 2009. Analysis was conducted August 2015. The MDD was considered persistent if patients had at least moderate depressive symptoms (IDS) at 2-year follow-up; otherwise, the MDD was considered remitted. MAIN OUTCOMES AND MEASURES: Sparse network structures of baseline MDD symptoms assessed via IDS were computed. Global and local connectivity of network structures were compared across persisters and remitters using a permutation test. RESULTS: Among the 515 patients, 335 (65.1%) were female, mead (SD) age was 40.9 (12.1) years, and 253 (49.1%) had persistent MDD at 2-year follow-up. Persisters (n = 253) had a higher baseline IDS sum score than remitters (n = 262) (mean SD score, 40.2 8.9 vs 35.1 7.1; the test statistic for the difference in IDS sum score was 22 027; P < .001). The test statistic for the difference in network connectivity was 1.79 (P = .01) for the original data, 1.55 for data matched on IDS sum score (P = .04), and 1.65 for partialed out data (P = .02). At the symptom level, fatigue or loss of energy and feeling guilty had the largest difference in importance in persisters’ network compared with that of remitters (Cohen d = 1.13 and 1.18, respectively). CONCLUSIONS AND RELEVANCE: This study reports that symptom networks of patients with MDD are related to longitudinal course: persisters exhibited a more densely connected network at baseline than remitters. More pronounced associations between symptoms may be an important determinant of persistence in MDD.
We present the R package mgm for the estimation of k-order mixed graphical models (MGMs) and mixed vector autoregressive (mVAR) models in high-dimensional data. These are a useful extensions of ...graphical models for only one variable type, since data sets consisting of mixed types of variables (continuous, count, categorical) are ubiquitous. In addition, we allow to relax the stationarity assumption of both models by introducing time-varying versions of MGMs and mVAR models based on a kernel weighting approach. Time-varying models offer a rich description of temporally evolving systems and allow to identify external influences on the model structure such as the impact of interventions. We provide the background of all implemented methods and provide fully reproducible examples that illustrate how to use the package.
The small world of psychopathology Borsboom, Denny; Cramer, Angélique O J; Schmittmann, Verena D ...
PloS one,
11/2011, Volume:
6, Issue:
11
Journal Article
Peer reviewed
Open access
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).
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.
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.
Network models are an increasingly popular way to abstract complex psychological phenomena. While studying the
structure
of network models has led to many important insights, little attention has ...been paid to how well they
predict
observations. This is despite the fact that predictability is crucial for judging the
practical relevance
of edges: for instance in clinical practice, predictability of a symptom indicates whether an intervention on that symptom through the symptom network is promising. We close this methodological gap by introducing nodewise predictability, which quantifies how well a given node can be predicted by all other nodes it is connected to in the network. In addition, we provide fully reproducible code examples of how to compute and visualize nodewise predictability both for cross-sectional and time series data.
Network analysis is entering fields where network structures are unknown, such as psychology and the educational sciences. A crucial step in the application of network models lies in the assessment ...of network structure. Current methods either have serious drawbacks or are only suitable for Gaussian data. In the present paper, we present a method for assessing network structures from binary data. Although models for binary data are infamous for their computational intractability, we present a computationally efficient model for estimating network structures. The approach, which is based on Ising models as used in physics, combines logistic regression with model selection based on a Goodness-of-Fit measure to identify relevant relationships between variables that define connections in a network. A validation study shows that this method succeeds in revealing the most relevant features of a network for realistic sample sizes. We apply our proposed method to estimate the network of depression and anxiety symptoms from symptom scores of 1108 subjects. Possible extensions of the model are discussed.
Networks are gaining popularity as an alternative to latent variable models for representing psychological constructs. Whereas latent variable approaches introduce unobserved common causes to explain ...the relations among observed variables, network approaches posit direct causal relations between observed variables. While these approaches lead to radically different understandings of the psychological constructs of interest, recent articles have established mathematical equivalences that hold between network models and latent variable models. We argue that the fact that for any model from one class there is an equivalent model from the other class does not mean that both models are equally plausible accounts of the data-generating mechanism. In many cases the constraints that are meaningful in one framework translate to constraints in the equivalent model that lack a clear interpretation in the other framework. Finally, we discuss three diverging predictions for the relation between zero-order correlations and partial correlations implied by sparse network models and unidimensional factor models. We propose a test procedure that compares the likelihoods of these models in light of these diverging implications. We use an empirical example to illustrate our argument.
Comorbidity: a network perspective Cramer, Angélique O J; Waldorp, Lourens J; van der Maas, Han L J ...
The Behavioral and brain sciences
33, Issue:
2-3
Journal Article
Peer reviewed
The pivotal problem of comorbidity research lies in the psychometric foundation it rests on, that is, latent variable theory, in which a mental disorder is viewed as a latent variable that causes a ...constellation of symptoms. From this perspective, comorbidity is a (bi)directional relationship between multiple latent variables. We argue that such a latent variable perspective encounters serious problems in the study of comorbidity, and offer a radically different conceptualization in terms of a network approach, where comorbidity is hypothesized to arise from direct relations between symptoms of multiple disorders. We propose a method to visualize comorbidity networks and, based on an empirical network for major depression and generalized anxiety, we argue that this approach generates realistic hypotheses about pathways to comorbidity, overlapping symptoms, and diagnostic boundaries, that are not naturally accommodated by latent variable models: Some pathways to comorbidity through the symptom space are more likely than others; those pathways generally have the same direction (i.e., from symptoms of one disorder to symptoms of the other); overlapping symptoms play an important role in comorbidity; and boundaries between diagnostic categories are necessarily fuzzy.
Moderated Network Models Haslbeck, Jonas M. B.; Borsboom, Denny; Waldorp, Lourens J.
Multivariate behavioral research,
03/2021, Volume:
56, Issue:
2
Journal Article
Peer reviewed
Open access
Pairwise network models such as the Gaussian Graphical Model (GGM) are a powerful and intuitive way to analyze dependencies in multivariate data. A key assumption of the GGM is that each pairwise ...interaction is independent of the values of all other variables. However, in psychological research, this is often implausible. In this article, we extend the GGM by allowing each pairwise interaction between two variables to be moderated by (a subset of) all other variables in the model, and thereby introduce a Moderated Network Model (MNM). We show how to construct MNMs and propose an
-regularized nodewise regression approach to estimate them. We provide performance results in a simulation study and show that MNMs outperform the split-sample based methods Network Comparison Test (NCT) and Fused Graphical Lasso (FGL) in detecting moderation effects. Finally, we provide a fully reproducible tutorial on how to estimate MNMs with the R-package mgm and discuss possible issues with model misspecification.
•Network analysis can foster novel insights in personality psychology.•We provide an overview of network analysis.•We show how R can be used to analyze personality networks.•We show how to simulate ...personality networks in R.
Network analysis represents a novel theoretical approach to personality. Network approaches motivate alternative ways of analyzing data, and suggest new ways of modeling and simulating personality processes. In the present paper, we provide an overview of network analysis strategies as they apply to personality data. We discuss different ways to construct networks from typical personality data, show how to compute and interpret important measures of centrality and clustering, and illustrate how one can simulate on networks to mimic personality processes. All analyses are illustrated using a data set on the commonly used HEXACO questionnaire using elementary R-code that readers may easily adapt to apply to their own data.
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