This study introduces a novel model that effectively captures asymmetric structures in multivariate contingency tables with ordinal categories. Leveraging the principle of maximum entropy, our approach employs f-divergence to provide a rational model under the presence of a ``prior guess.'' Inspired by the constraints used in the derivation of multivariate normal distributions, we demonstrate that the proposed model minimizes f-divergence from complete symmetry under specific constraints. The proposed model encompasses existing asymmetry models as special cases while offering remarkably high interpretability. By modifying divergence measures included in f-divergence, the model provides the flexibility to adapt to specific probabilistic structures of interest. Furthermore, we established theorems that show that a complete symmetry model can be decomposed into two or more models, each imposing less restrictive parameter constraints. We also investigated the properties of the goodness-of-fit statistics with an emphasis on the likelihood ratio and Wald test statistics. Extensive Monte Carlo simulations confirmed the nominal size, high power, and robustness of the choice of f-divergence. Finally, an application to real-world data highlights the practical utility of the proposed model for analyzing asymmetric structures in ordinal contingency tables.

翻译：本研究提出了一种新颖的模型，可有效捕捉具有序数类别的多元列联表中的非对称结构。基于最大熵原理，我们的方法利用f-散度在存在“先验猜测”的情况下构建合理模型。受多元正态分布推导中约束条件的启发，我们证明了所提模型在特定约束下可最小化与完全对称性的f-散度。该模型将现有非对称模型作为特例包含其中，同时具备极高的可解释性。通过调整f-散度中的散度度量，模型能灵活适应特定概率结构。此外，我们建立了定理证明完全对称模型可分解为两个或多个参数约束更宽松的模型，并重点研究了似然比检验与Wald检验统计量的拟合优度统计特性。大量蒙特卡洛模拟验证了f-散度选择的标称性、高效力及稳健性。最后，通过实际数据应用展示了该模型在分析序数列联表非对称结构方面的实用价值。