Generalized marginal cumulative logistic model for multi-way contingency tables

For multi-way contingency tables of same classifications with or- dered categories, this paper proposes two generalized marginal cumulative logis- tic models. Those indicate that the difference between two marginal cumulative logits, or two conditional marginal cumulative logits on condition that all val- ues 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. AMS 2010 Mathematics Subject Classication. 62H17.