<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Studies have been carried out on decomposing a model with symmetric structure using a model with asymmetric structure. In the existing decomposition theorem, the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and concordancediscordance models hold. However, this existing decomposition theorem does not satisfy the asymptotic equivalence for the test statistic, namely that the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the decomposed models. To address this issue, this study introduces a new decomposition theorem in which the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic—the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models.</p>
</abstract>

Studies have been carried out on decomposing a model with symmetric structure using a model with asymmetric structure. In the existing decomposition theorem, the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and concordancediscordance models hold. However, this existing decomposition theorem does not satisfy the asymptotic equivalence for the test statistic, namely that the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the decomposed models. To address this issue, this study introduces a new decomposition theorem in which the sum-symmetry model holds if and only if all of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic—the value of the likelihood ratio chi-squared statistic of the sum-symmetry model is asymptotically equivalent to the sum of those of the two-parameters sum-symmetry, global symmetry and weighted global-sum-symmetry models.

Orthogonal decomposition of the sum-symmetry model using the two-parameters sum-symmetry model for ordinal square contingency tables

Department of Information and Computer Technology, Faculty of Engineering

Biometrical Letters

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Studies have been carried out on decomposing a model with symmetric structure using a model with asymmetric structure. In the existing decomposition theorem,...

Orthogonal decomposition of the sum-symmetry model using the two-parameters sum-symmetry model for ordinal square contingency tables

Published Online: Dec 30, 2021

Page range: 105 - 117

DOI: https://doi.org/10.2478/bile-2021-0008

Keywords
asymptotic equivalence, asymmetry, orthogonality, symmetry, test statistic

© 2020 Shuji Ando, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Orthogonal decomposition of the sum-symmetry model using the two-parameters sum-symmetry model for ordinal square contingency tables

Published Online: Dec 30, 2021

Page range: 105 - 117

DOI: https://doi.org/10.2478/bile-2021-0008

Keywordsasymptotic equivalence, asymmetry, orthogonality, symmetry, test statistic

© 2020 Shuji Ando, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
asymptotic equivalence, asymmetry, orthogonality, symmetry, test statistic