Visualizing departures from marginal homogeneity for square contingency tables with ordered categories

TL;DR

This paper introduces a novel visualization method for analyzing departures from marginal homogeneity in square contingency tables with ordered categories, using a new measure based on Matusita distance.

Contribution

The paper proposes a new visualization technique and a Matusita distance-based measure for better interpretation of marginal homogeneity analysis in categorical data tables.

Findings

Effective visualization of MH departures demonstrated through multiple examples

The new measure provides intuitive insights into categorical data analysis

Validation shows improved interpretability over existing measures

Abstract

Square contingency tables are a special case commonly used in various fields to analyze categorical data. Although several analysis methods have been developed to examine marginal homogeneity (MH) in these tables, existing measures are single-summary ones. To date, a visualization approach has yet to be proposed to intuitively depict the results of MH analysis. Current measures used to assess the degree of departure from MH are based on entropy such as the Kullback-Leibler divergence and do not satisfy distance postulates. Hence, the current measures are not conducive to visualization. Herein we present a measure utilizing the Matusita distance and introduce a visualization technique that employs sub-measures of categorical data. Through multiple examples, we demonstrate the meaningfulness of our visualization approach and validate its usefulness to provide insightful interpretations.