A1667
Title: Power-divergence-based measures approximating latent correlation in contingency tables under bivariate normality
Authors: Wataru Urasaki - Tokyo University of Science (Japan) [presenting]
Abstract: Association measures for two-way contingency tables play an important role in the analysis of ordinal categorical data, where one primary goal is to quantify the strength of association beyond testing independence. Although many divergence-based measures have been proposed, their values are not always easy to interpret in relation to familiar correlation coefficients. In many applications, observed categories may also be regarded as discretizations of underlying continuous variables, making latent correlation a natural target of interpretation. Building on a previously established closed-form approximation, the power-divergence from independence under bivariate normality is expressed as a function of the latent correlation coefficient. By inverting this relationship, a family of power-divergence-based association measures is obtained that reflects latent correlation while retaining the computational simplicity of divergence-based methods. The resulting framework includes classical measures, such as Linfoot's informational measure and Pearson's contingency coefficient, as special cases. Asymptotic distributions and confidence intervals are also derived through the delta method. The methodological background, theoretical properties, and practical advantages of the proposed measures for contingency table analysis are presented, together with a brief report on numerical experiments.
