A two-dimensional index for marginal homogeneity in ordinal square contingency tables

Abstract

For square contingency tables with ordered categories, indexes that represent the degree of departure from the marginal homogeneity (MH) model have been proposed. There are two types of directionalities of departure from MH. The existing indexes, however, can analyze either the degree of departure from MH or the directionality but not both. To address this issue, this study proposes a two-dimensional index, which combines the existing indexes, can simultaneously analyze both the degree and directionality of departure from MH. This study also evaluates the usefulness of the proposed index for visually comparing degrees of departure from MH in several square contingency tables using confidence region.