Correspondence Analysis for Assessing Departures from Perfect Symmetry Using the Cressie–Read Family of Divergence Statistics

Abstract

Recently, Beh and Lombardo (2022, Symmetry, 14, 1103) showed how to perform a correspondence analysis on a two-way contingency table where Bowker’s statistic lies at the numerical heart of this analysis. Thus, we showed how this statistic could be used to visually identify departures from perfect symmetry. Interestingly, Bowker’s statistic is a special case of the symmetry version of the Cressie–Read family of divergence statistics. Therefore, this paper presents a new framework for visually assessing departures from perfect symmetry using a second-order Taylor series approximation of the Cressie–Read family of divergence statistics.

Keywords

• Bowker’s chi-squared statistic
• correspondence analysis
• Cressie–Read family of divergence statistics
• singular value decomposition