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Tying up the loose ends in simple correspondence analysis


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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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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 940.

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Date of creation: Jan 2006
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Handle: RePEc:upf:upfgen:940

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Keywords: Biplot; bootstrapping; canonical correlation; chi-square distance; confidence; ellipse; contingency table; convex hull; correspondence analysis; inertia; randomization test; rotation; singular value;

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  1. K. Ruben Gabriel, 2002. "Goodness of fit of biplots and correspondence analysis," Biometrika, Biometrika Trust, Biometrika Trust, vol. 89(2), pages 423-436, June.
  2. J. Aitchison & Michael Greenacre, 2001. "Biplots of compositional data," Economics Working Papers 557, Department of Economics and Business, Universitat Pompeu Fabra.
  3. Michael Greenacre, 2008. "Correspondence analysis of raw data," Economics Working Papers 1112, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2009.
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Cited by:
  1. Marie Chavent & Vanessa Kuentz-Simonet & Jérôme Saracco, 2012. "Orthogonal rotation in PCAMIX," Advances in Data Analysis and Classification, Springer, Springer, vol. 6(2), pages 131-146, July.
  2. 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, Elsevier, vol. 53(8), pages 3117-3128, June.
  3. 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.
  4. Urbano Lorenzo-Seva & Michel van de Velden & Henk A. L. Kiers, . "CAR: A MATLAB Package to Compute Correspondence Analysis with Rotations," Journal of Statistical Software, American Statistical Association, American Statistical Association, vol. 31(i08).


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