10 - Nonstandard Log-Linear Models for Measuring Change in Categorical Variables

Abstract

This chapter presents nonstandard log-linear models for two well-known tests and log-linear models for axial symmetry and quasi-symmetry. First, three equivalent forms of Bower's symmetry test are considered. The chapter also discusses the Model of Parallel Axial Symmetry as one example of how to incorporate symmetry testing in multi-group comparisons. The model proposes that axial symmetry holds across two or more groups of subjects. Differences in group size can be considered, and so can assumptions that constrain axial symmetry to specific pairs of cells. Additional extensions include models for more than two observation points. F The design matrix approach allows researchers to analyze data without having to create three-dimensional tables. There are benefits beyond the presentation of equivalent forms and beyond didactical advances. Thus, researchers can identify those pairs of cells for which symmetry holds and those for which symmetry is violated.