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 as a prior distribution on the network structure of a graphical model for binary and ordinal data. The stochastic block model assumes that variables belong to latent clusters, where the probability of an edge depends on the cluster membership of the nodes. Embedding this model 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 membership of the nodes from cross-sectional data. We illustrate the performance of the method in a simulation study and apply it to a reanalysis of 30 empirical datasets.