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The association in two-way ordinal contingency tables through global odds ratios

Author

Listed:
  • Ida Camminatiello

    (University of Campania L. Vanvitelli Corso Gran Priorato di Malta)

  • Antonello D’Ambra

    (University of Campania L. Vanvitelli Corso Gran Priorato di Malta)

  • Luigi D’Ambra

    (University of Napoli Federico II Monte Sant’Angelo)

Abstract

Hirotsu’s statistic is a suitable measure for studying the association between two variables on an ordinal scale. For visualizing the nature of the association, such a statistic can be decomposed by performing doubly ordered cumulative correspondence analysis. An alternative measure for describing the association between two ordered variables could be global odds ratios. In this paper we consider a generalization of the doubly ordered cumulative correspondence analysis in order to represent the global odds ratios in the two-dimensional plot.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metron:v:80:y:2022:i:1:d:10.1007_s40300-021-00224-7
    DOI: 10.1007/s40300-021-00224-7
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    References listed on IDEAS

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    1. Mark Rooij & Willem Heiser, 2005. "Graphical representations and odds ratios in a distance-association model for the analysis of cross-classified data," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 99-122, March.
    2. Greenacre, Michael, 2009. "Power transformations in correspondence analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3107-3116, June.
    3. 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.
    4. 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.
    5. 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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