# Bayesian Clustering Factor Models

## TL;DR

This paper introduces a new Bayesian method that combines dimension reduction and clustering to better understand complex data patterns.

## Contribution

The novel Bayesian clustering factor model framework allows simultaneous dimension reduction and clustering with uncertainty quantification.

## Key findings

- The proposed Gibbs sampler effectively explores the posterior distribution.
- The information criterion performs well in selecting the correct number of clusters and factors.
- The framework is successfully applied to opioid use disorder recovery data for personalized healthcare insights.

## 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 two previously published competitor methods, 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.