ASYMMETRY MODELS BASED ON LOGIT TRANSFORMATIONS FOR SQUARE CONTINGENCY TABLES WITH ORDINAL CATEGORIES

Abstract

Many observations tend to concentrate in the main diagonal cells when analyzing square contingency tables with ordered categories. Although many statisticians have proposed a variety of symmetry and asymmetry models, constraints on the main diagonal cells are not considered. This implies that the observed frequencies on the main diagonal cells are not utilized. Herein we propose three models that indicate an asymmetric structure for the log odds ratio for cell probabilities. These models constrain the main diagonal cells such that the information in the main diagonal cells can be utilized. Then we decompose the symmetry model using the proposed models.