Modeling a mixture of ordinal and continuous repeated measures

We study the correlation structure for a mixture of ordinal and continuous repeated measures using a Bayesian approach. We assume a multivariate probit model for the ordinal variables and a normal linear regression for the continuous variables, where latent normal variables underlying the ordinal data are correlated with continuous variables in the model. Due to the probit model assumption, we are required to sample a covariance matrix with some of the diagonal elements equal to one. The key computational idea is to use parameter-extended data augmentation, which involves applying the Metropolis-Hastings algorithm to get a sample from the posterior distribution of the covariance matrix incorporating the relevant restrictions. The methodology is illustrated through a simulated example and through an application to data from the UCLA Brain Injury Research Center.