NONSTANDARD LOG-LINEAR MODELS

This article demonstrates several useful varieties of nonstandard log-linear models. Some can be derived as nonhierarchical models by deleting lower-order effects in hierarchical models, but most often they will arise as the result of special hypotheses that the researcher wants to test. Three approaches to testing nonstandard models-partitioning chi-square, creating homogeneous subgroups, and the model matrix approach-are illustrated on a variety of data sets. It is assumed that the reader has been exposed to the general area of log-linear models, is familiar with dummy and effect coding of categorical variables in the usual regression framework, and knows how to express models in matrix form. A brief summary of the standard approach to log-linear models and of coding methods is provided for readers needing a review.