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...

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Published inBulletin - Calcutta Statistical Association Vol. 71; no. 2; pp. 83 - 98
Main Authors Yoshimoto, Takuya, Tahata, Kouji, Iki, Kiyotaka, Tomizawa, Sadao
Format Journal Article
LanguageEnglish
Japanese
Published New Delhi, India SAGE Publications 01.11.2019
Subjects
square contingency table
Decomposition
Covariance
symmetry
moment
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Summary: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
ISSN:0008-0683
2456-6462
DOI:10.1177/0008068319880443