Generalized marginal cumulative logistic model for multi-way contingency tables

Abstract

For multi-way contingency tables of same classifications with ordered categories, this paper proposes two generalized marginal cumulative logistic models. Those indicate that the difference between two marginal cumulative logits, or two conditional marginal cumulative logits on condition that all values of the variables are not identical, is a polynomial function of the category value. This paper also gives a theorem that the marginal homogeneity model holds if and only if both the proposed model and moment equality model hold. An example is given.