Abstract
For two-way contingency tables, Tomizawa (1985) considered the quasi point-symmetry (QP) model and the marginal point-symmetry (MP) model, and gave the theorem that the point-symmetry (PS) model holds if and only if both the QP and MP models hold. Tahata and Tomizawa (2008) provided similar theorems for multi-way tables. For multi-way tables, the present paper proposes the quasi point-symmetry (QP[]) model based on -divergence. The QP[] model includes the QP model in a special case. It also gives the theorem that the PS model holds if and only if both the QP[] and MP models hold, and the theorem that the test statistic for goodness-of-fit of the PS model is asymptotically equivalent to the sum of those for the decomposed models under the PS model.
Acknowledgments
The authors are greatly thankful to the referee and editor for their helpful and valuable suggestions to further improve this article.
Citation
Takuya Yoshimoto. Kouji Tahata. Yusuke Saigusa. Sadao Tomizawa. "Quasi point-symmetry models based on -divergence and decomposition of point-symmetry for multi-way contingency tables." SUT J. Math. 55 (2) 109 - 137, December 2019. https://doi.org/10.55937/sut/1577359452
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