 Correspondence analysis

Correspondence analysis (CA) is a multivariate statistical technique proposed^{[1]} by Hirschfeld^{[2]} and later developed by JeanPaul Benzécri.^{[3]} It is conceptually similar to principal component analysis, but applies to categorical rather than continuous data. In a similar manner to principal component analysis, it provides a means of displaying or summarising a set of data in twodimensional graphical form.
All data should be nonnegative and on the same scale for CA to be applicable, and the method treats rows and columns equivalently. It is traditionally applied to contingency tables — CA decomposes the chisquare statistic associated with this table into orthogonal factors. Because CA is a descriptive technique, it can be applied to tables whether or not the chisquare statistic is appropriate.^{[4]}^{[5]} Several variants of CA are available, including detrended correspondence analysis and canonical correspondence analysis. The extension of correspondence analysis to many categorical variables is called multiple correspondence analysis. An adaptation of correspondence analysis to the problem of discrimination based upon qualitative variables (i.e., the equivalent of discriminant analysis for qualitative data) is called discriminant correspondence analysis or barycentric discriminant analysis.
In the social sciences, correspondence analysis, and particularly its extension multiple correspondence analysis, was made known outside France through French sociologist Pierre Bourdieu's application of it.^{[citation needed]}
Implementations
 Orange, a free data mining software suite, module orngCA
 In the open source statistical package R, the packages
ade4
,ca
^{[6]},vegan,
, and[1]FactoMineR
implement correspondence analysis and multiple correspondence analysis.  Here is a link to a MATLAB program (with a tutorial) for correspondence analysis: http://www.utdallas.edu/~herve/abdiCorrespondenceAnalysisMatlabProgram.zip
References
 ^ Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP ISBN 0198509944
 ^ Hirschfeld, H.O. (1935) "A connection between correlation and contingency", Proc. Cambridge Philosophical Society, 31, 520–524
 ^ Benzécri, J.P. (1973). L'Analyse des Données. Volume II. L'Analyse des Correspondances. Paris, France: Dunod.
 ^ Greenacre, Michael (1983). Theory and Applications of Correspondence Analysis. London: Academic Press. ISBN 0122990501.
 ^ Greenacre, Michael (2007). Correspondence Analysis in Practice, Second Edition. London: Chapman & Hall/CRC.
 ^ Nenadic, O. and Greenacre, M. (2007) "Correspondence analysis in R, with two and threedimensional graphics: the ca package", Journal of Statistical Software, 20(3)
External links
 Greenacre, Michael (2008), La Práctica del Análisis de Correspondencias, BBVA Foundation, Madrid, Spanish translation of Correspondence Analysis in Practice, available for free download from BBVA Foundation publications
 Greenacre, Michael (2010), Biplots in Practice, BBVA Foundation, Madrid, available for free download at multivariatestatistics.org
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