Correspondence analysis

Correspondence analysis

Correspondence analysis (CA) is a multivariate statistical technique proposed[1] by Hirschfeld[2] and later developed by Jean-Paul 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 two-dimensional 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 chi-square statistic associated with this table into orthogonal factors. Because CA is a descriptive technique, it can be applied to tables whether or not the chi-square 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]



  1. ^ Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP ISBN 0-19-850994-4
  2. ^ Hirschfeld, H.O. (1935) "A connection between correlation and contingency", Proc. Cambridge Philosophical Society, 31, 520–524
  3. ^ Benzécri, J.-P. (1973). L'Analyse des Données. Volume II. L'Analyse des Correspondances. Paris, France: Dunod. 
  4. ^ Greenacre, Michael (1983). Theory and Applications of Correspondence Analysis. London: Academic Press. ISBN 0-12-299050-1. 
  5. ^ Greenacre, Michael (2007). Correspondence Analysis in Practice, Second Edition. London: Chapman & Hall/CRC. 
  6. ^ Nenadic, O. and Greenacre, M. (2007) "Correspondence analysis in R, with two- and three-dimensional 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

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