Advances in Quasi-Symmetry for Square Contingency Tables

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Abstract

Contingency tables highlight relationships between categorical variables. Typically, the symmetry or marginal homogeneity of a square contingency table is evaluated. The original symmetry model often does not accurately fit a dataset due to its restrictions. Caussinus proposed a quasi-symmetry model which served as a bridge between symmetry and marginal homogeneity in square contingency tables. This study significantly influenced methodological developments in the statistical analysis of categorical data. Herein recent advances in quasi-symmetry are reviewed with an emphasis on four topics related to the author’s results: (1) modeling based on the f-divergence, (2) the necessary and sufficient condition of symmetry, (3) partition of test statistics for symmetry, and (4) measure of the departure from symmetry. The asymmetry model based on f-divergence enables us to express various asymmetries. Additionally, these models are useful to derive the necessary and sufficient conditions of symmetry with desirable properties. This review may be useful to consider the statistical modeling and the measure of symmetry for contingency tables with the same classifications.

Original languageEnglish
Article number1051
JournalSymmetry
Volume14
Issue number5
DOIs
Publication statusPublished - May 2022

Keywords

  • decomposition
  • f-divergence
  • marginal homogeneity
  • measure
  • symmetry

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