Advancements in marginal modeling for categorical data

Very often the data collected by social scientists involve dependent observations, without, however, the investigators having any substantive interest in the nature of the dependencies. Although these dependencies are not important for the answers to the research questions concerned, they must still be taken into account in the analysis. Standard statistical estimation and testing procedures assume independent and identically distributed observations, and they need to be modified for observations that are clustered in some way. Marginal models provide the tools to deal with these dependencies without having to make restrictive assumptions about their nature. In this paper, recent developments in the (maximum likelihood) estimation and testing of marginal models for categorical data will be explained, including marginal models with latent variables. The differences and commonalities with other ways of dealing with these nuisance dependencies will be discussed, especially with GEE and also briefly with (hierarchical) random coefficient models. The usefulness of marginal modeling will be illuminated by showing several common types of research questions and designs for which marginal models may provide the answers, along with two extensive real world examples. Finally, a brief evaluation will be given, including a discussion of shortcomings and strong points as well as computer programs and future work to be done.