2024/05/20 by Hisaya Okahara, Okahara, Hisaya, Kouji Tahata +1
Computer Science · Decision Sciences · Mathematics · #Advanced Causal Inference Techniques #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Methodology (stat.ME) #Reliability and Agreement in Measurement
paper · pdf · doi:10.48550/arxiv.2405.12157
openalex publication_date 2024/05/20 · openalex created_date 2024/05/22 · openalex updated_date 2026/07/31
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.