Bayesian Analysis of the Ordinal Markov Random Field

Multivariate analysis using graphical models is rapidly gaining ground in psychology. In particular, Markov Random Field (MRF) graphical models have become popular because their graph structure reflects the conditional associations between psychological variables. Despite the fact that most psychological variables are assessed on an ordinal scale, the analysis of MRFs for ordinal variables has received little attention in the psychometric literature. To fill this gap, we present an MRF for ordinal data that so far has not been considered in network psychometrics. We present statistical methodology to test the structure of the proposed MRF, which requires us to determine the plausibility of the opposing hypotheses of conditional dependence and independence. To this end, we develop a Bayesian approach using the inclusion Bayes factor to quantify the (lack of) evidence for a given edge. We use a Bayesian variable selection approach to model the inclusion and exclusion of edges in the network, and Bayesian model averaging to compare network structures with and without the given edge. We provide an implementation in the new R package bgms, evaluate its performance in simulations, and illustrate it with empirical data.