Parameter-expanded data augmentation for analyzing categorical data using multinomial probit models.

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The multinomial probit model is a popular tool for examining nominal categorical data. However, due to the model's identification issue which requires restricting the first element of the covariance matrix of the latent variables, it poses a daunting challenge for researchers to develop efficient Markov chain Monte Carlo (MCMC) methods. The parameter-expanded data augmentation (PX-DA) is a well-known technique that introduces a working/artificial parameter or parameter vectors to transform an identifiable model into a non-identifiable one. This transformation can improve the mixing and convergence of the data augmentation components. Hence, we propose a PX-DA algorithm to analyze the categorical data using multinomial probit models. We examine both identifiable and non-identifiable multinomial probit models and develop the corresponding MCMC algorithms. The constructed non-identifiable model successfully bypasses a Metropolis-Hastings algorithm for sampling the covariance matrix, resulting in enhanced convergence and improved mixing of the MCMC components. We conduct simulation studies to demonstrate our proposed methods and apply them to the real data from the Six Cities study.

multinomial probit model

latent variable

parameter-expanded

data augmentation

MCMC

non-identifiable model 

Section on Bayesian Statistical Science