Introduction

Abstract

The starting point for the marginal modeling of categorical data is a multidimensional table representing the joint probability distribution of two or more categorical variables. Over the last decades, many techniques have been developed to analyze the relationships in such a table, excellent overviews of which have been provided by Agresti at several levels of difficulty (Agresti, 1990, 1996, 2002). Very often, however, researchers are not interested in the analysis of the complete joint distribution but in a marginal analysis, i.e., in the comparison of two or more marginal tables that may be formed from the original complete table by collapsing cells. In the first section of this chapter, the concept ofmarginalmodeling of categorical data will be further explained, partly and briefly in contrast to alternative approaches that deal with more or less related research problems (as already mentioned in the Preface). Thereafter, some historical background will be provided, identifying previous statistical work on testing marginal homogeneity, and some statistical approaches that can be seen as forms of marginal modeling but are usually not explicitly identified as such. In the final section of this chapter, several descriptive statistics are introduced that are used in the remainder of this book to describe and test particular differences between marginal distributions.