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Abstract: Multivariate probit models have been explored for analyzing longitudinal ordinal data. However, the inherent identification issue in multivariate probit models requires the covariance matrix of the underlying latent multivariate normal variables to be a correlation matrix and thus hinders the development of efficient Bayesian sampling methods. It is known that non-identifiable models may produce Markov chain Monte Carlo (MCMC) samplers with better convergence and mixing than identifiable models. Therefore, we were motivated to construct a non-identifiable multivariate probit model and to develop efficient MCMC sampling algorithms. In comparison with the MCMC sampling algorithm based on the identifiable multivariate probit model, which requires a Metropolis-Hastings (MH) algorithm for sampling a correlation matrix, our proposed MCMC sampling algorithms based on the non-identifiable model circumvent an MH algorithm by a Gibbs sampler for sampling a covariance matrix and thus accelerate the MCMC convergence. We illustrate our proposed methods using simulation studies and two real data applications.

Bio: Dr. Xiao Zhang is an Assistant Professor in Mathematical Sciences at Michigan Technological University. Her areas of expertise include: Bayesian computation, Missing data analysis, Longitudinal and multivariate data analysis, Survival analysis, Multi-state modeling and Statistical genetics. Dr. Zhang received her B.S. in Mathematics from Shandong Normal University, China.. She continued on to receive her MS in Probability and Statistics from Beijing University, China. Her degree pursuit was complete with a PhD in Biostatistics from the University of California—Los Angeles.