Statistical models for the analysis of ordered categorical data in public health and medical research

In the late 1970s statisticians extended the methods for analysing loglinear and logit models for cross-classified categorical data to incorporate information about the ordinal structure of the categories corresponding to some of the classification variables. In this paper we review one class of such extensions known as association models. We consider association models with and without order restrictions on the parameters and we use these models to answer research questions about several medical examples involving ordered categorical data. We emphasize the interpretation of parameters in the association models and how this relates to the research questions of interest.