Biometrical Letters Vol. 58(2), 2021, pp. 95-104
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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 Shuji Ando Department of Information and Computer Technology, Faculty of Engineering, Tokyo University of Science, Katsushika-ku, Tokyo, 125-8585, Japan, e-mail: shuji.ando@rs.tus.ac.jp |
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.
matched-pairs data, orthogonality, sum-symmetry model, test statistic
