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Weighted cumulative correspondence analysis based on a particular cumulative power divergence family

Author

Listed:
  • Antonello D’Ambra

    (University of Campania “L.Vanvitelli”)

  • Giovanni Meccariello

    (Institute of Sciences and Technologies for Sustainable Energy and Mobility)

  • Livia Della Ragione

    (Institute of Sciences and Technologies for Sustainable Energy and Mobility)

Abstract

The Pearson’s $$X^2$$ X 2 statistic and the likelihood ratio statistic $$G^2$$ G 2 are most frequently used for testing independence or homogeneity, in two-way contingency table. These indexes are members of a continuous family of Power Divergence (PD) statistics, but they perform badly in studying the association between ordinal categorical variables. Taguchi’s and Nair’s statistics have been introduced in the literature as simple alternatives to Pearson’s index for contingency tables with ordered categorical variables. It’s possible to show, using a parameter, how to link Taguchi’s and Nair’s statistics obtaining a new class called Weighted Cumulative Chi-Squared (WCCS-type tests). Therefore, the main aim of this paper is to introduce a new divergence family based on cumulative frequencies called Weighted Cumulative Power Divergence. Moreover, an extension of Cumulative Correspondence Analysis based on WCCS and further properties are shown.

Suggested Citation

  • Antonello D’Ambra & Giovanni Meccariello & Livia Della Ragione, 2024. "Weighted cumulative correspondence analysis based on a particular cumulative power divergence family," Annals of Operations Research, Springer, vol. 342(3), pages 1407-1428, November.
    • Handle: RePEc:spr:annopr:v:342:y:2024:i:3:d:10.1007_s10479-022-04718-z
    DOI: 10.1007/s10479-022-04718-z
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    References listed on IDEAS

    as
    1. Antonello D’Ambra & Pietro Amenta, 2011. "Correspondence Analysis with Linear Constraints of Ordinal Cross-Classifications," Journal of Classification, Springer;The Classification Society, vol. 28(1), pages 70-92, April.
    2. Pasquale Sarnacchiaro & Antonello D'ambra, 2007. "Explorative Data Analysis and CATANOVA for Ordinal Variables: An Integrated Approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(9), pages 1035-1050.
    3. Rosaria Lombardo & Eric Beh & Antonello D'Ambra, 2011. "Studying the dependence between ordinal-nominal categorical variables via orthogonal polynomials," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2119-2132.
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