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Studying the dependence between ordinal-nominal categorical variables via orthogonal polynomials

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  • Rosaria Lombardo
  • Eric Beh
  • Antonello D'Ambra

Abstract

In situations where the structure of one of the variables of a contingency table is ordered recent theory involving the augmentation of singular vectors and orthogonal polynomials has shown to be applicable for performing symmetric and non-symmetric correspondence analysis. Such an approach has the advantage of allowing the user to identify the source of variation between the categories in terms of components that reflect linear, quadratic and higher-order trends. The purpose of this paper is to focus on the study of two asymmetrically related variables cross-classified to form a two-way contingency table where only one of the variables has an ordinal structure.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:10:p:2119-2132
    DOI: 10.1080/02664763.2010.545118
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    References listed on IDEAS

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    1. Rosaria Lombardo & Pieter Kroonenberg & Luigi D’Ambra, 2000. "Non-symmetric correspondence analysis and biplot representation: Comparing differences in market share distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 9(1), pages 107-126, January.
    2. Lombardo, R. & Beh, E.J. & D'Ambra, L., 2007. "Non-symmetric correspondence analysis with ordinal variables using orthogonal polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 566-577, September.
    3. 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.
    4. Rosaria Lombardo & Eric Beh, 2010. "Simple and multiple correspondence analysis for ordinal-scale variables using orthogonal polynomials," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(12), pages 2101-2116.
    5. Kenneth Berry & Janis Johnston & Paul Mielke, 2009. "Exact and resampling probability values for the Piccarreta nominal-ordinal index of association," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(11), pages 1239-1249.
    6. Raffaella Piccarreta, 2001. "A new measure of nominal-ordinal association," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(1), pages 107-120.
    7. Eric Beh & Luigi D’Ambra, 2009. "Some Interpretative Tools for Non-Symmetrical Correspondence Analysis," Journal of Classification, Springer;The Classification Society, vol. 26(1), pages 55-76, April.
    8. Shizuhiko Nishisato & P. Arri, 1975. "Nonlinear programming approach to optimal scaling of partially ordered categories," Psychometrika, Springer;The Psychometric Society, vol. 40(4), pages 525-548, December.
    9. Rosaria Lombardo & Jacqueline Meulman, 2010. "Multiple Correspondence Analysis via Polynomial Transformations of Ordered Categorical Variables," Journal of Classification, Springer;The Classification Society, vol. 27(2), pages 191-210, September.
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    Citations

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    Cited by:

    1. 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.
    2. Eric J. Beh & Rosaria Lombardo, 2018. "An algebraic generalisation of some variants of simple correspondence analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(4), pages 423-443, May.

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