Bayesian Analysis of Longitudinal Ordinal Data with Missing Values Using Multivariate Probit Models

In this paper, we propose efficient Bayesian methods to analyze longitudinal ordinal data with missing values using multivariate probit models. Longitudinal ordinal data with substantial missing values are ubiquitous in many scientific fields. Specifically, we develop the Markov chain Monte Carlo (MCMC) sampling methods based on the non-identifiable multivariate probit models and further compare their performance with the one based on the identifiable multivariate probit models. We carried out our investigation through simulation studies, which show that the proposed methods can handle substantial missing values and the method with marginalizing the redundant parameters based on the non-identifiable model outperforms the others in the mixing and convergences of the MCMC sampling components. We then present an application using data from the Russia Longitudinal Monitoring Survey-Higher School of Economics (RLMS-HSE).