A Stochastic Block Prior for Clustering in Graphical Models

Graphical models facilitate the representation of psychological variables as complex systems of interacting variables structured as a network. However, their current statistical estimation procedures overlook the assumption of clustering, which refers to the grouping of subsets of variables that are more densely connected within the network, despite this assumption playing a central role in many psychological theories. We address this gap by proposing the use of the Stochastic Block Model (SBM) as a prior distribution on the network structure of a graphical model for binary and ordinal data. The SBM assumes that variables belong to latent clusters, where the probability of an edge depends on the cluster membership of the nodes. Embedding this prior in a Bayesian graphical modeling framework allows researchers to formally incorporate theoretical expectations about clustering, test hypotheses about the number of clusters, and estimate cluster assignments from cross-sectional data. We demonstrate the benefits of this approach in a simulation study and reanalyze 30 openly available empirical datasets to test for clustering. This work highlights how the Bayesian framework can embed theoretical assumptions into network models via priors and introduces a new tool for latent cluster inference in psychological network analysis.