Moment Symmetry Models and Decompositions of Symmetry for Multi-way Contingency Tables

Abstract

For square contingency tables, Caussinus^[1] demonstrated that the symmetry model holds if and only if both the quasi-symmetry and marginal homogeneity models hold. Bishop, Fienberg, and Holland^{[2, p. 307]} and Bhapkar and Darroch^[3] provided similar theorems for multi-way tables. The present article proposes a moment symmetry model and unique decompositions of the symmetry model. For two-way tables, the second-order moment symmetry model decomposes the symmetry model into the second-order moment symmetry and marginal homogeneity models, while the $h$ th-order moment symmetry model decomposes the $h$ th-order marginal symmetry model using the $h - 1$ th-order marginal symmetry model for multi-way tables.

AMS 2000 subject classification: 62H17

Keywords

Covariance Decomposition moment square contingency table symmetry

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