Bayesian Clustering Factor Models

We present a novel framework for concomitant dimension reduction and clustering. This framework is based on a novel class of Bayesian clustering factor models. These models assume a factor model structure where the vectors of common factors follow a mixture of Gaussian distributions. We develop a Gibbs sampler to explore the posterior distribution and propose an information criterion to select the number of clusters and the number of factors. Simulation studies show that our inferential approach appropriately quantifies uncertainty. In addition, when compared to a previously published competitor method, our information criterion has favorable performance in terms of correct selection of number of clusters and number of factors. Finally, we illustrate the capabilities of our framework with an application to data on recovery from opioid use disorder where clustering of individuals may facilitate personalized health care.