Correspondence Analysis Using the Cressie–Read Family of Divergence Statistics

Abstract

The foundations of correspondence analysis rests with Pearson's chi-squared statistic. More recently, it has been shown that the Freeman–Tukey statistic plays an important role in correspondence analysis and confirmed the advantages of the Hellinger distance that have long been advocated in the literature. Pearson's and the Freeman–Tukey statistics are two of five commonly used special cases of the Cressie–Read family of divergence statistics. Therefore, this paper explores the features of correspondence analysis where its foundations lie with this family and shows that log-ratio analysis (an approach that has gained increasing attention in the correspondence analysis and compositional data analysis literature) and the method based on the Hellinger distance are special cases of this new framework.