Log-linear modeling

This article describes log-linear models as special cases of generalized linear models. Specifically, log-linear models use a logarithmic link function. Log-linear models are used to examine joint distributions of categorical variables, dependency relations, and association patterns. Three types of log-linear models are discussed, hierarchical models, nonhierarchical models, and nonstandard models. Emphasis is placed on parameter interpretation. It is demonstrated that parameters are best interpretable when they represent the effects specified in the design matrix of the model. Parameter interpretation is illustrated first for a standard hierarchical model, and then for a nonstandard model that includes structural zeros. In a data example, the relationships among race of defendant, race of victim, and death penalty sentence are examined using a log-linear model with all three two-way interactions. Recent developments in log-linear modeling are discussed.