Decompositions of Marginal Homogeneity Model Using Cumulative Logistic Models for Multi-Way Contingency Tables

Abstract

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. Miyamoto, Niibe and Tomizawa (2005) proposed the conditional marginal cumulative logistic (CML) model which is defined off the main diagonal cells, and gave the decompositions of the MH model using the ML (CML) model. This paper (1) considers the ML and CML models for multi-way tables, and (2) gives the decompositions of the MH model into the ML (CML) model and the model of the equality of marginal means for multi-way tables. An example is given.