Previously, the diagonals-parameter symmetry model based on $f$-divergence (denoted by DPS[$f$]) was reported to be equivalent to the diagonals-parameter symmetry model regardless of the function $f$, but the proof was omitted. Here, we derive the DPS[$f$] model and the proof of the relation between the two models. We can obtain various interpretations of the diagonals-parameter symmetry model from the result. Additionally, the necessary and sufficient conditions for symmetry and property between test statistics for goodness of fit are discussed.

翻译：此前，基于$f$-散度的对角线参数对称模型（记为DPS[$f$]）被报道为与函数$f$无关的对角线参数对称模型等价，但该证明被省略。本文推导了DPS[$f$]模型并给出了两个模型之间关系的证明。由此结果可获得对角线参数对称模型的多重解释。此外，本文还讨论了对称性的充要条件以及拟合优度检验统计量之间的性质。