Bayesian Clustering Factor Models

TL;DR

This paper introduces a Bayesian clustering factor model framework that combines dimension reduction and clustering, with a novel inference method and application to healthcare data.

Contribution

It proposes a new Bayesian model with an efficient Gibbs sampler and an information criterion for selecting the number of clusters and factors.

Findings

Accurately quantifies uncertainty in clustering and factor analysis.

Favorable performance in selecting the correct number of clusters and factors.

Demonstrates practical application to opioid use disorder data.

Abstract

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.