Identifiability and convergence behavior for Markov chain Monte Carlo using multivariate probit models

Xiao Zhang

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 14, 4600-4615

Abstract: Multivariate probit models have been popularly utilized to analysis multivariate ordinal data. However, the identifiable multivariate probit models entail the covariance matrix for the underlying multivariate normal variables to be a correlation matrix, which brings a rigorous task to conduct efficient statistical analysis. Parameter expansion to make the identifiable model to be non-identifiable has been inevitably explored. However, the effect of the expanded parameters on the convergence of Markov chain Monte Carlo (MCMC) is seldomly investigated; in addition, the comparison of MCMC developed based on the identifiable model and that based on the non-identifiable model is hardly ever explored, especially for data with large sample sizes. In this paper, we conduct a thorough investigation to illustrate the effect of the expanded parameters on the convergence of MCMC and compare the behavior of MCMC between the identifiable and non-identifiable models. Our investigation provides a practical guide regarding the construction of non-identifiable models and development of corresponding MCMC sampling methods. We conduct our investigation using simulation studies and present an application using data from the Russia Longitudinal Monitoring Survey-Higher School of Economics (RLMS-HSE) study.

Date: 2025
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DOI: 10.1080/03610926.2024.2425738

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