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

TL;DR

This paper presents a new flexible model using f-divergence to effectively capture asymmetry in multivariate ordinal contingency tables, improving interpretability and adaptability over existing models.

Contribution

It introduces a novel maximum entropy-based f-divergence model for asymmetric ordinal tables, encompassing existing models and allowing divergence measure modifications for specific structures.

Findings

Model effectively captures asymmetry in ordinal tables.

High power and robustness confirmed through simulations.

Practical utility demonstrated with real data application.

Abstract

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.