ABSTRACT
This chapter examines the model-building approach to loglinear and logit models. These comprise another special case of generalized linear models designed for contingency tables of frequencies. They are most easily interpreted through visualizations, including mosaic displays and effect plots of associated logit models. Loglinear models have been developed from two formally distinct, but related perspectives. The first is a discrete analog of familiar ANOVA models for quantitative data, where the multiplicative relations among joint and marginal probabilities are transformed into an additive one by transforming the counts to logarithms. Fitting a loglinear model is usually a process of deciding which association terms are large enough to warrant inclusion in a model to explain the observed frequencies. Logit models, on the other hand, describe how the log odds for one variable depends on other, explanatory variables. Cells with frequencies of zero create problems for loglinear and logit models.
