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For square contingency tables with ordered categories, Agresti (1984, 2002) considered the marginal cumulative logistic (ML) model, which is an extension of the marginal homogeneity (MH) model. The ML model depends on the probabilities on the main diagonal of the table. This paper (1) proposes the conditional marginal cumulative logistic (CML) model which does not depend on the probabilities on the main diagonal, and (2) decomposes the MH model into the ML (CML) model and the model which indicates the equality of row and column marginal means. Examples are given.

Decompositions of Marginal Homogeneity Model Using Cumulative Logistic Models for Square Contingency Tables with Ordered Categories