Without Pain -- Clustering Categorical Data Using a Bayesian Mixture of Finite Mixtures of Latent Class Analysis Models

TL;DR

This paper introduces a Bayesian clustering method for multivariate categorical data that models variable associations within clusters and determines the number of clusters automatically, using a two-layer mixture of finite mixtures with latent class analysis.

Contribution

It presents a novel Bayesian two-layer mixture model with a specific prior setup and MCMC estimation for clustering categorical data, addressing variable association and unknown cluster count.

Findings

Demonstrates effective clustering performance in simulation studies.

Shows good results on a real low back pain dataset.

Highlights importance of hyperparameter selection for shrinkage.

Abstract

We propose a Bayesian approach for model-based clustering of multivariate categorical data where variables are allowed to be associated within clusters and the number of clusters is unknown. The approach uses a two-layer mixture of finite mixtures model where the cluster distributions are approximated using latent class analysis models. A careful specification of priors with suitable hyperparameter values is crucial to identify the two-layer structure and obtain a parsimonious cluster solution. We outline the Bayesian estimation based on Markov chain Monte Carlo sampling with the telescoping sampler and describe how to obtain an identified clustering model by resolving the label switching issue. Empirical demonstrations in a simulation study using artificial data as well as a data set on low back pain indicate the good clustering performance of the proposed approach, provided hyperparameters are selected which induce sufficient shrinkage.