Measures of Departure from Local Marginal Homogeneity for Square Contingency Tables

Abstract

When focusing on changes in political party support, it is crucial to determine whether or not there has been a change in the aggregate. From this perspective, various types of marginal homogeneity models have been proposed. We propose local marginal homogeneity models, which indicate that there are symmetric structures of probabilities for only one pair of symmetric marginal probabilities or cumulative probabilities. In addition, we propose two measures, one for nominal categories and one for ordered categories, to express the degree of departure from local marginal homogeneity models. We also apply the measures to data and confirm that the measures help compare the degree of departure from the model in several tables.