Parameter-Expanded Data Augmentation for Analyzing Nominal Data With Missing Values Using Multinomial Probit Models

Nominal data occur in many scientific fields, such as health-related studies, transportation, and econometrics. Due to the ubiquitousness of missing data, it is inevitable to analyze nominal data with missing values. As is well known, statistical methods for analyzing nominal variables are quite limited. The Multinomial Probit (MNP) model has been an essential tool for analyzing nominal categorical data, but the computational complexity of maximum likelihood functions and stringent model identification bring a rigorous task for both likelihood-based estimation and Markov Chain Monte Carlo (MCMC) sampling, hence confine the utilization of this important model. Advanced developments in Bayesian computation have shown the promising performance of Parameter-Expanded Data Augmentation (PX-DA) in MCMC sampling. Accordingly, in this investigation, we propose PX-DA to analyze nominal data with missing values using MNP models. We conduct our investigation through simulation studies and an application to the Mental Health Client-Level Data. Our investigation demonstrates that the proposed methods significantly improve the convergence and mixing of MCMC sampling components and can handle nominal data with substantial missingness, and thus enhance the practical usage of MNP models in the field of discrete data analysis.