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., <i>n</i> = 1 time series), and a mixture of the 2 (e.g., <i>n</i> &gt; 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 <i>graphical VAR</i>. 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 <i>graphicalVAR</i> and <i>mlVAR</i>. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials.

Keywords

Affiliated Institutions

• University of Amsterdam NL
• University of Edinburgh GB

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