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An algebraic generalisation of some variants of simple correspondence analysis

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  • Eric J. Beh

    (University of Newcastle)

  • Rosaria Lombardo

    (University of Campania)

Abstract

For an analysis of the association between two categorical variables that are cross-classified to form a contingency table, graphical procedures have been central to this analysis. In particular, correspondence analysis has grown to be a popular method for obtaining such a summary and there is a great variety of different approaches that one may consider to perform. In this paper, we shall introduce a simple algebraic generalisation of some of the more common approaches to obtaining a graphical summary of association, where these approaches are akin to the correspondence analysis of a two-way contingency table. Specific cases of the generalised procedure include the classical and non-symmetrical correspondence plots and the symmetrical and isometric biplots.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:4:d:10.1007_s00184-018-0649-0
    DOI: 10.1007/s00184-018-0649-0
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    References listed on IDEAS

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    1. Michel Velden & Henk A.L. Kiers, 2005. "Rotation in Correspondence Analysis," Journal of Classification, Springer;The Classification Society, vol. 22(2), pages 251-271, September.
    2. Vartan Choulakian, 1988. "Exploratory analysis of contingency tables by loglinear formulation and generalizations of correspondence analysis," Psychometrika, Springer;The Psychometric Society, vol. 53(2), pages 235-250, June.
    3. 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.
    4. John Aitchison & Michael Greenacre, 2002. "Biplots of compositional data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 375-392, October.
    5. Vartan Choulakian, 1988. "Exploratory analysis of contingency tables by loglinear formulation and generalizations of correspondence analysis," Psychometrika, Springer;The Psychometric Society, vol. 53(4), pages 593-593, December.
    6. 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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