A Bivariate Index for Visually Measuring Marginal Inhomogeneity in Square Tables

Abstract

For square tables, the marginal homogeneity model which has a structure that the row marginal distribution is equal to the column marginal distribution was proposed. Thereafter, various extended models of marginal homogeneity have been proposed, these models can be classified into two types marginal inhomogeneity. On the other hand, various indexes which measure the degree of deviation from marginal homogeneity have been proposed. However these indexes cannot concurrently define degrees of deviation from marginal homogeneity with respect to two types marginal inhomogeneity. This paper proposes a bivariate index that can concurrently define degrees of deviation from those. The proposed bivariate index would also be utility for visually comparing degrees of deviation from marginal homogeneity in several tables using confidence regions.