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

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.