Bayes Factor Tests for Group Differences in Ordinal and Binary Graphical Models

Multivariate analysis of psychological variables using graphical models has become a standard analysis in the psychometric literature. Most cross-sectional measures are either binary or ordinal, and the methodology for inferring the structure of networks of binary and ordinal variables is developing rapidly. In practice, however, research questions often focus on whether and how networks differ between observed groups. While Bayes factor methods for inferring network structure are well established, a similar methodology for assessing group differences in networks of binary or ordinal variables is currently lacking. In this paper, we extend the Bayesian framework for the analysis of ordinal Markov random fields, a network model for binary and ordinal variables, and develop Bayes factor tests for assessing parameter differences in the networks of two independent groups. The proposed methods are implemented in the R package \texttt{bgms}, and we use numerical illustrations to show that the implemented methods work correctly and how well the methods work compared to existing methods in situations resembling empirical research.