Likelihood analysis of the multivariate ordinal probit regression model for repeated ordinal responses

We consider the analysis of longitudinal ordinal data, meaning regression-like analysis when the response variable is categorical with ordered categories, and is measured repeatedly over time (or space) on the experimental or sampling units. Particular attention is given to the multivariate ordinal probit regression model, in which the correlation between ordered categorical responses on the same unit at different times (or locations) is modeled with a latent variable that has a multivariate normal distribution. An algorithm for maximum likelihood analysis of this model is proposed and the analysis is demonstrated on an example. Simulations clarify the extent to which maximum likelihood estimators can be more efficient than generalized estimating equations (GEE) estimators of regression coefficients and the extent to which likelihood ratio tests can be more accurate than tests based on standard errors and approximate normality of GEE estimators.