Modeling Cross-Classified Categorical Data

In this chapter we introduce some of the basic terminology and concepts for fitting loglinear models to cross-classified categorical data. We discuss briefly those aspects of model fitting relevant to the development of further chapters, and we show how the power-divergence statistic adds a new dimension to categorical data analysis. In addition, Section 3.4 describes methods of estimating unknown model parameters from the perspective of the power-divergence statistic. In Section 3.5 we discuss the minimum discrimination information approach to characterizing the loglinear model, and illustrate how the power-divergence statistic provides a generalization that characterizes other models (including the linear model). The chapter concludes with a discussion in Section 3.6 of strategies for choosing an appropriate loglinear model.