Abstract: Many popular methods for the analysis of serial measurements obtained in longitudinal studies are based on an underlying multivariate normal distribution with linear mean model for the observations. By modeling the convariance matrix separately from the mean, a broad class of correlation structures can be accommodated. Since the multivariate normal is parameterized only by the mean and covariance of the observations, likelihood-based and moment-based estimation approaches yield similar estimating equations. When the longitudinal responses obtained are categorical, the data structures are similar, but developing flexible model-based approaches which parallel the general linear multivariate normal model is more complex because of two general features of categorical data: the dependence of variance on the mean and the attractiveness of nonlinear models for the mean response. This paper discusses two approaches to modeling these data structures, a general multivariate and a random effects model. We draw parallels with the serial measurements case, and consider the interpretation of the parameters in the model. We discuss maximum likelihood estimation of model parameters under the full likelihood and, for the random effects model, using a conditional likelihood.
Key words and phrases: Repeated categorical response, random effects models, multivariate models for discrete responses.