1. bookVolume 58 (2021): Issue 2 (December 2021)
Journal Details
License
Format
Journal
eISSN
2199-577X
First Published
17 Aug 2013
Publication timeframe
2 times per year
Languages
English
access type Open Access

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

Published Online: 30 Dec 2021
Volume & Issue: Volume 58 (2021) - Issue 2 (December 2021)
Page range: 105 - 117
Journal Details
License
Format
Journal
eISSN
2199-577X
First Published
17 Aug 2013
Publication timeframe
2 times per year
Languages
English
Summary

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.

Keywords

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