Composite mixture of log-linear models for categorical data

TL;DR

This paper introduces a new Bayesian approach called Mills, which combines latent class analysis and log-linear models to effectively model complex, sparse multivariate categorical data with improved flexibility and interpretability.

Contribution

It proposes a novel mixture of log-linear models (Mills) that integrates latent class analysis for better handling of high-dimensional sparse categorical data.

Findings

Mills outperforms traditional methods in simulations.

Application demonstrates insights into suicide attempts and empathy.

Provides a flexible, interpretable modeling framework.

Abstract

Multivariate categorical data are routinely collected in many application areas. As the number of cells in the table grows exponentially with the number of variables, many or even most cells will contain zero observations. This severe sparsity motivates appropriate statistical methodologies that effectively reduce the number of free parameters, with penalized log-linear models and latent structure analysis being popular options. This article proposes a fundamentally new class of methods, which we refer to as Mixture of Log Linear models (mills). Combining latent class analysis and log-linear models, mills defines a novel Bayesian methodology to model complex multivariate categorical with flexibility and interpretability. Mills is shown to have key advantages over alternative methods for contingency tables in simulations and an application investigating the relation among suicide attempts and empathy.