Marginal Cumulative Logistic Model of General Order for Multi-way Contingency Tables

Abstract

For multi-way contingency table, Bhapkar and Darroch (1990) considered the marginal symmetry model for order h. The present paper proposes a marginal cumulative logistic model for order h. When h=1, this model reduces to the marginal logistic model (Agresti, 2002). It also gives a theorem that the marginal symmetry model for order h holds if and only if (i) the marginal cumulative logistic model for order h, (ii) the marginal moment equality model for order h, and (iii) the marginal symmetry model for order h-1 hold. A special case of this theorem with h=1 is identical to the result of Tahata, Katakura and Tomizawa (2007).