Quasi point-symmetry models based on f-divergence and decomposition of point-symmetry for multi-way contingency tables

Takuya Yoshimoto, Kouji Tahata, Yusuke Saigusa, Sadao Tomizawa

Research output: Contribution to journalArticle


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[f]) model based on f-divergence. The QP[f] 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[f] 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.

Original languageEnglish
Pages (from-to)109-137
Number of pages29
JournalSUT Journal of Mathematics
Issue number2
Publication statusPublished - 1 Jan 2019



  • Marginal point-symmetry
  • Orthogonality
  • Square contingency table

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