The Gaussian Graphical Model in Cross-sectional and Time-series Data

TL;DR

This paper explores the Gaussian graphical model (GGM) as a versatile tool for analyzing various psychological datasets, including cross-sectional, time-series, and multi-subject data, highlighting its utility in uncovering variable relationships and causal structures.

Contribution

It introduces estimation methods for GGM in different data types, including time-series and multi-subject data, and provides practical implementations in R packages with empirical examples.

Findings

GGM effectively models relationships in psychological data.

The methods are implemented in R packages graphicalVAR and mlVAR.

Empirical examples demonstrate GGM's utility in real datasets.

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 3 kinds of psychological datasets: datasets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered datasets (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.