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

Abstract

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.

The Study of Psychopathology from the Network Analysis Perspective: A Systematic Review

“…Many authors have mentioned the use of cross-sectional data as a limitation and point out the need to carry out longitudinal studies to be able to discern the directionality of the associations in the network [42, 48, 49, 59, 60] as well as temporal prediction [97]. For example, in our review there are only 3 studies using longitudinal data of psychotic symptoms of which only 1 uses ESM measures (online suppl.…”

Dynamic Network Analysis of Negative Emotions and DSM‐5 Posttraumatic Stress Disorder Symptom Clusters During Conflict

“…Missing data within completed assessments was very low (13 of 4,273 assessments). For the analyses, we removed all pairs of lagged and current variables that contained missing responses (Epskamp et al., ). Of the final sample, 70.8% participants ( n = 68) were female, and the average participant age was 30.1 years ( SD = 9.0).…”

“…Dynamic network analysis uses a multilevel vector autoregression (multilevel VAR) model, in which each variable is regressed on all the variables in the network from the previous assessment while using a multilevel structure to account for clustering within individuals (Bringmann et al., ; Epskamp et al., ). This model produces three networks: temporal, contemporaneous, and between‐persons.…”

“…In the current study, this showed the within‐measurement associations between negative emotions and PTSD clusters. Lastly, the between‐persons network depicts the covariance between stationary means of different individuals (Epskamp et al., ). In this paper, we focus on the temporal and contemporaneous networks; the between‐persons network is shown in Supplementary Figure S1.…”

“…In the last few years, network analysis has been extended to a multilevel framework, using intensive longitudinal data gathered through ESM to estimate dynamic networks (Bodner, Kuppens, Allen, Sheeber, & Ceulemans, ; Bos et al., ; Bringmann et al., ; Epskamp, Waldorp, Mõttus, & Borsboom, ; Greene, Gelkopf, Epskamp, & Fried, ; Lydon‐Staley, Xia, Mak, & Fosco, ; Pe et al., ). Dynamic networks could provide useful insights into potentially predictive associations between components by the estimation of directed temporal networks, in which the direction of the association between network components from moment to moment can be depicted (Bringmann et al., ).…”