<p>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 <i>f</i>-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 <i>f</i>-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 <i>f</i>-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 <i>f</i>-divergence. Finally, an application to real-world data highlights the practical utility of the proposed model for analyzing asymmetric structures in ordinal contingency tables.</p>

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Modeling asymmetry in multi-way contingency tables with ordinal categories via f-divergence

  • Hisaya Okahara,
  • Kouji Tahata

摘要

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.