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A dimensional reduction method for ordinal three-way contingency table

In: Compstat 2006 - Proceedings in Computational Statistics

Author

Listed:
  • Luigi D’Ambra

    (Universita’ di Napoli, Dip. di Matematica e Statistica)

  • Biagio Simonetti

    (Universita’ di Napoli, Dip. di Matematica e Statistica)

  • Eric J. Beh

    (University of Western Sydney, School of Computing and Mathematics)

Abstract

For the study of association in three-way, and more generally multi-way, contingency tables the literature offers a large number of techniques that can be considered. When there is an asymmetric dependence structure between the variables the Marcotorchino index [Mar84] (as apposed to the Pearson chi-squared statistic) can be used to measure the strength of their association. When the variables have an ordinal structure, this information is often not take into account. In this paper we introduce a partition of the Marcotorchino index for three ordered categorical variables using a special class of orthogonal polynomials. A graphical procedure is also considered to obtain a visual summary of the asymmetrical relationship between the variables.

Suggested Citation

  • Luigi D’Ambra & Biagio Simonetti & Eric J. Beh, 2006. "A dimensional reduction method for ordinal three-way contingency table," Springer Books, in: Alfredo Rizzi & Maurizio Vichi (ed.), Compstat 2006 - Proceedings in Computational Statistics, pages 271-283, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-1709-6_21
    DOI: 10.1007/978-3-7908-1709-6_21
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