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

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Multiple correspondence analysis — In statistics, multiple correspondence analysis (MCA) is a data analysis technique for nominal categorical data, used to detect and represent underlying structures in a data set. It does this by representing data as points in a low dimensional… …   Wikipedia

  • Detrended correspondence analysis — (DCA) is a multivariate statistical technique widely used by ecologists to find the main factors or gradients in large, species rich but usually sparse data matrices that typify ecological community data. For example, Hill and Gauch (1980, p. 55) …   Wikipedia

  • Detrended Correspondence Analysis — (DCA) is a multivariate statistical technique widely used by ecologists to find the main factors or gradients in large, species rich but usually sparse data matrices that typify ecological community data. For example, Hill and Gauch (1980, p. 55) …   Wikipedia

  • Correspondence — may refer to: In general usage, non concurrent, remote communication between people, including letters, email, newsgroups, Internet forums, blogs Correspondence theory of truth (philosophy), a theory in epistemology Correspondence principle… …   Wikipedia

  • Analysis of categorical data — These are statistical procedures which can be used for the analysis of categorical data:* regression * analysis of variance * linear modeling * log linear modeling * logistic regression * repeated measures analysis * simple correspondence… …   Wikipedia

  • Correspondence Publishing Committee — was a radical left organization led by C.L.R. James and Martin Glaberman that existed in the United States from approximately 1951 until it split in 1962. Contents 1 History 2 Facing Reality 3 Sources …   Wikipedia

  • Correspondence chess — Postcard for international correspondence chess Correspondence chess is chess played by various forms of long distance correspondence, usually through a correspondence chess server, through email or by the postal system; less common methods which …   Wikipedia

  • Correspondence law school — Main article: Law school A correspondence law school is a school that offers legal education by distance education, either by correspondence or online by use of the internet, or a combination thereof. Contents 1 Germany 2 South Africa 3 United… …   Wikipedia

  • Correspondence principle — This article discusses quantum theory and relativity. For other uses, see Correspondence principle (disambiguation). In physics, the correspondence principle states that the behavior of systems described by the theory of quantum mechanics (or by… …   Wikipedia

  • Correspondence of Charles Darwin — Charles Darwin in 1854 The British naturalist Charles Darwin had correspondence with numerous other luminaries of his age and members of his family. These have provided many insights about the nineteenth century, from scientific exploration and… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”