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Orthogonal decomposition of the sum-symmetry model for square contingency tables with ordinal categories: Use of the exponential sum-symmetry model

Authors
  • Ando, Shuji1
  • 1 Tokyo University of Science, Katsushika-ku, Tokyo, 125-8585 , (Japan)
Type
Published Article
Journal
Biometrical Letters
Publisher
Sciendo
Publication Date
Dec 01, 2021
Volume
58
Issue
2
Pages
95–104
Identifiers
DOI: 10.2478/bile-2021-0007
Source
De Gruyter
Keywords
License
Green

Abstract

In the existing decomposition theorem, the sum-symmetry model holds if and only if both the exponential sum-symmetry and global symmetry models hold. However, this decomposition theorem does not satisfy the asymptotic equivalence for the test statistic. To address the aforementioned gap, this study establishes a decomposition theorem in which the sum-symmetry model holds if and only if both the exponential sum-symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic. We demonstrate the advantages of the proposed decomposition theorem by applying it to datasets comprising real data and artificial data.

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