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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ISSN0008-0683
2456-6462
DOI10.1177/0008068319880443

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Abstract 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
AbstractList 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
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
Author Sadao Tomizawa
Kiyotaka Iki
Takuya Yoshimoto
Kouji Tahata
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Cites_doi 10.1007/978-0-387-71887-3
10.1080/01621459.1979.10481650
10.1002/0471249688
10.1016/0047-259X(90)90034-F
10.1109/TAC.1974.1100705
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Keywords square contingency table
Decomposition
Covariance
symmetry
moment
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Snippet Abstract For square contingency tables, Caussinus[1] demonstrated that the symmetry model holds if and only if both the quasi-symmetry and marginal homogeneity...
For square contingency tables, Caussinus [ 1 ] demonstrated that the symmetry model holds if and only if both the quasi-symmetry and marginal homogeneity...
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Title Moment Symmetry Models and Decompositions of Symmetry for Multi-way Contingency Tables
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