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 [Formula: see text]th-order moment symmetry model decomposes the [Formula: see text]th-order marginal symmetry model using the [Formula: see text]th-order marginal symmetry model for multi-way tables. AMS 2000 subject classification: 62H17

Parsimonious Bivariate T-distribution Type Symmetry Models for Square Contingency Tables

“…The symmetry (S) model (Bowker, 1948), the marginal homogeneity model (Stuart, 1955) and the quasi-symmetry model (Caussinus, 1965) have been proposed as models of symmetry. Moreover, for the research of the symmetry model, see Yoshimoto et al (2019), Ando et al (2021) and Shinoda et al (2021).…”