### 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[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 language | English |
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Pages (from-to) | 109-137 |

Number of pages | 29 |

Journal | SUT Journal of Mathematics |

Volume | 55 |

Issue number | 2 |

Publication status | Published - 1 Jan 2019 |

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### Keywords

- Marginal point-symmetry
- Orthogonality
- Square contingency table

### Cite this

*SUT Journal of Mathematics*,

*55*(2), 109-137.