Asymmetry Model Using Marginal Ridits for Ordinal Square Contingency Tables

Abstract

This study proposes a new marginal asymmetry model which can infer the relation between marginal ridits of row and column variables for ordinal square contingency tables. When the marginal homogeneity model does not hold, we will apply marginal asymmetry models (e.g., the marginal cumulative logistic and extended marginal homogeneity models). On the other hand, we may measure the degree of departure from the marginal homogeneity model. To measure the degree of that, multiple indexes were proposed. Some of them correspond to the marginal cumulative logistic and extended marginal homogeneity models. The proposed model corresponds to the index, which represents the degree of departure from the MH model, using marginal ridits. We compare the proposed model with the existing marginal asymmetry models and show that the proposed model provides better fit performance than them for real data.