IDEAS home Printed from https://ideas.repec.org/a/bla/istatr/v92y2024i1p17-42.html
   My bibliography  Save this article

Correspondence Analysis Using the Cressie–Read Family of Divergence Statistics

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/insr.12541
    Download Restriction: no
    File URL: https://libkey.io/10.1111/insr.12541?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Greenacre, Michael, 2009. "Power transformations in correspondence analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3107-3116, June.
    3. McCullagh, Peter, 1984. "Generalized linear models," European Journal of Operational Research, Elsevier, vol. 16(3), pages 285-292, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Renata Pelissari & Sarah Ben Amor & Álvaro Oliveira D’Antona & Eduardo José Marandola Júnior & Leonardo Tomazeli Duarte, 2024. "A semi-supervised multi-criteria sorting approach to constructing social vulnerability composite indicators," Annals of Operations Research, Springer, vol. 337(1), pages 235-260, June.
    3. Tengyuan Liang & Weijie J. Su, 2019. "Statistical inference for the population landscape via moment‐adjusted stochastic gradients," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 431-456, April.
    4. Blasius, J. & Greenacre, M. & Groenen, P.J.F. & van de Velden, M., 2009. "Special issue on correspondence analysis and related methods," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3103-3106, June.
    5. Christian E. Galarza & Panpan Zhang & Víctor H. Lachos, 2021. "Logistic Quantile Regression for Bounded Outcomes Using a Family of Heavy-Tailed Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 325-349, November.
    6. Ida Camminatiello & Antonello D’Ambra & Luigi D’Ambra, 2022. "The association in two-way ordinal contingency tables through global odds ratios," METRON, Springer;Sapienza Università di Roma, vol. 80(1), pages 9-22, April.
    7. Michael Greenacre, 2023. "The chi-square standardization, combined with Box-Cox transformation, is a valid alternative to transforming to logratios in compositional data analysis," Economics Working Papers 1857, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Trond Petersen, 1986. "Estimating Fully Parametric Hazard Rate Models with Time-Dependent Covariates," Sociological Methods & Research, , vol. 14(3), pages 219-246, February.
    9. Rodrigues Teixeira, Ana Carolina & Machado, Pedro Gerber & Borges, Raquel Rocha & Felipe Brito, Thiago Luis & Moutinho dos Santos, Edmilson & Mouette, Dominique, 2021. "The use of liquefied natural gas as an alternative fuel in freight transport – Evidence from a driver's point of view," Energy Policy, Elsevier, vol. 149(C).
    10. Michael Greenacre & Paul Lewi, 2009. "Distributional Equivalence and Subcompositional Coherence in the Analysis of Compositional Data, Contingency Tables and Ratio-Scale Measurements," Journal of Classification, Springer;The Classification Society, vol. 26(1), pages 29-54, April.
    11. Christine Howard & Emma-Liina Marjakangas & Alejandra Morán-Ordóñez & Pietro Milanesi & Aleksandre Abuladze & Karen Aghababyan & Vitalie Ajder & Volen Arkumarev & Dawn E. Balmer & Hans-Günther Bauer &, 2023. "Local colonisations and extinctions of European birds are poorly explained by changes in climate suitability," Nature Communications, Nature, vol. 14(1), pages 1-12, December.
    12. William H. Greene & David A. Hensher, 2008. "Modeling Ordered Choices: A Primer and Recent Developments," Working Papers 08-26, New York University, Leonard N. Stern School of Business, Department of Economics.
    13. Warnick, Benjamin J. & Davis, Blakley C. & Allison, Thomas H. & Anglin, Aaron H., 2021. "Express yourself: Facial expression of happiness, anger, fear, and sadness in funding pitches," Journal of Business Venturing, Elsevier, vol. 36(4).
    14. Anglin, Aaron H. & Short, Jeremy C. & Drover, Will & Stevenson, Regan M. & McKenny, Aaron F. & Allison, Thomas H., 2018. "The power of positivity? The influence of positive psychological capital language on crowdfunding performance," Journal of Business Venturing, Elsevier, vol. 33(4), pages 470-492.
    15. Lombardo, Rosaria & Camminatiello, Ida & D'Ambra, Antonello & Beh, Eric J., 2021. "Assessing the Italian tax courts system by weighted three-way log-ratio analysis," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    16. Tajvarpour, Mohammad Hossein & Pujari, Devashish, 2022. "The influence of narrative description on the success of crowdfunding campaigns: The moderating role of quality signals," Journal of Business Research, Elsevier, vol. 149(C), pages 123-138.
    17. Tsai, Arthur C. & Liou, Michelle & Simak, Maria & Cheng, Philip E., 2017. "On hyperbolic transformations to normality," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 250-266.
    18. Zahra Faraji-Dana & Fred Tam & J Jean Chen & Simon J Graham, 2016. "Suppressing Respiration Effects when Geometric Distortion Is Corrected Dynamically by Phase Labeling for Additional Coordinate Encoding (PLACE) during Functional MRI," PLOS ONE, Public Library of Science, vol. 11(6), pages 1-19, June.
    19. Coro, Gianpaolo & Magliozzi, Chiara & Vanden Berghe, Edward & Bailly, Nicolas & Ellenbroek, Anton & Pagano, Pasquale, 2016. "Estimating absence locations of marine species from data of scientific surveys in OBIS," Ecological Modelling, Elsevier, vol. 323(C), pages 61-76.
    20. Wan-Yu Liu & Pin-Zheng Chen & Chi-Ming Hsieh, 2019. "Assessing the Recreational Value of a National Forest Park from Ecotourists’ Perspective in Taiwan," Sustainability, MDPI, vol. 11(15), pages 1-17, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:istatr:v:92:y:2024:i:1:p:17-42. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/isiiinl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.