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Correspondence Analysis Using the Cressie–Read Family of Divergence Statistics

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  • Eric J. Beh
  • Rosaria Lombardo

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.

Suggested Citation

  • Eric J. Beh & Rosaria Lombardo, 2024. "Correspondence Analysis Using the Cressie–Read Family of Divergence Statistics," International Statistical Review, International Statistical Institute, vol. 92(1), pages 17-42, April.
    • Handle: RePEc:bla:istatr:v:92:y:2024:i:1:p:17-42
    DOI: 10.1111/insr.12541
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    References listed on IDEAS

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    1. McCullagh, Peter, 1984. "Generalized linear models," European Journal of Operational Research, Elsevier, vol. 16(3), pages 285-292, June.
    2. Beh, Eric J. & Lombardo, Rosaria & Alberti, Gianmarco, 2018. "Correspondence analysis and the Freeman–Tukey statistic: A study of archaeological data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 73-86.
    3. Greenacre, Michael, 2009. "Power transformations in correspondence analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3107-3116, June.
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    Cited by:

    1. Ting-Wu Wang & Eric J. Beh & Rosaria Lombardo & Ian W. Renner, 2025. "Profile transformations for reciprocal averaging and singular value decomposition," Computational Statistics, Springer, vol. 40(3), pages 1217-1251, March.

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