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Tying up the loose ends in simple correspondence analysis

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Abstract

Although correspondence analysis is now widely available in statistical software packages and applied in a variety of contexts, notably the social and environmental sciences, there are still some misconceptions about this method as well as unresolved issues which remain controversial to this day. In this paper we hope to settle these matters, namely (i) the way CA measures variance in a two-way table and how to compare variances between tables of different sizes, (ii) the influence, or rather lack of influence, of outliers in the usual CA maps, (iii) the scaling issue and the biplot interpretation of maps,(iv) whether or not to rotate a solution, and (v) statistical significance of results.

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  • Michael Greenacre, 2006. "Tying up the loose ends in simple correspondence analysis," Economics Working Papers 940, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:940
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    References listed on IDEAS

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    1. Michael Greenacre, 2008. "Correspondence analysis of raw data," Economics Working Papers 1112, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2009.
    2. 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.
    3. K. Ruben Gabriel, 2002. "Goodness of fit of biplots and correspondence analysis," Biometrika, Biometrika Trust, vol. 89(2), pages 423-436, June.
    4. M. O. Hill, 1974. "Correspondence Analysis: A Neglected Multivariate Method," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 23(3), pages 340-354, November.
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    1. repec:jss:jstsof:31:i08 is not listed on IDEAS
    2. Lorenzo-Seva, Urbano & van de Velden, Michel & Kiers, Henk A. L., 2009. "CAR: A MATLAB Package to Compute Correspondence Analysis with Rotations," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i08).
    3. Michael Greenacre & Paul Lewi, 2009. "Distributional Equivalence and Subcompositional Coherence in the Analysis of Compositional Data, Contingency Tables and Ratio-Scale Measurements," Journal of Classification, Springer;The Classification Society, vol. 26(1), pages 29-54, April.
    4. Marie Chavent & Vanessa Kuentz-Simonet & Jérôme Saracco, 2012. "Orthogonal rotation in PCAMIX," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 6(2), pages 131-146, July.
    5. Lorenzo-Seva, U. & van de Velden, M. & Kiers, H.A.L., 2007. "Oblique rotation in correspondence analysis: a step forward in the simplest interpretation," Econometric Institute Research Papers EI 2007-25, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Polak, Marike & Heiser, Willem J. & de Rooij, Mark, 2009. "Two types of single-peaked data: Correspondence analysis as an alternative to principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3117-3128, June.

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    More about this item

    Keywords

    Biplot; bootstrapping; canonical correlation; chi-square distance; confidence; ellipse; contingency table; convex hull; correspondence analysis; inertia; randomization test; rotation; singular value;
    All these keywords.

    JEL classification:

    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software

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