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The Contributions of Rare Objects in Correspondence Analysis

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  • Michael Greenacre

Abstract

Correspondence analysis, when used to visualize relationships in a table of counts (for example, abundance data in ecology), has been frequently criticized as being too sensitive to objects (for example, species) that occur with very low frequency or in very few samples. In this statistical report we show that this criticism is generally unfounded. We demonstrate this in several data sets by calculating the actual contributions of rare objects to the results of correspondence analysis and canonical correspondence analysis, both to the determination of the principal axes and to the chi-square distance. It is a fact that rare objects are often positioned as outliers in correspondence analysis maps, which gives the impression that they are highly influential, but their low weight offsets their distant positions and reduces their effect on the results. An alternative scaling of the correspondence analysis solution, the contribution biplot, is proposed as a way of mapping the results in order to avoid the problem of outlying and low contributing rare objects.

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Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 571.

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Date of creation: Sep 2011
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Handle: RePEc:bge:wpaper:571

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Keywords: Biplot; canonical correspondence analysis; contribution; correspondence analysis; influence; outlier; scaling;

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  1. Michael Greenacre, 2009. "Contribution biplots," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 1162, Department of Economics and Business, Universitat Pompeu Fabra, revised Jan 2011.
  2. Michael Greenacre, 2008. "Correspondence analysis of raw data," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 1112, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2009.
  3. Oleg Nenadic & Michael Greenacre, . "Correspondence Analysis in R, with Two- and Three-dimensional Graphics: The ca Package," Journal of Statistical Software, American Statistical Association, American Statistical Association, vol. 20(i03).
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