Marginal modelling of multivariate categorical data

This paper describes likelihood methods of analysis for multivariate categorical data. The joint distribution is specified in terms of marginal mean functions, and pairwise and higher order association measures. For the association, the emphasis is on global odds ratios. The method allows flexible formulation of a broad class of designs, such as repeated measurements, longitudinal studies, interrater agreement and cross-over trials. The proposed model can be used for parameter estimation and hypothesis testing. Simple fitting algorithms are proposed. The method is illustrated using a data example.