From correspondence analysis to multiple and joint correspondence analysis
The generalization of simple (two-variable) correspondence analysis to more than two categorical variables, commonly referred to as multiple correspondence analysis, is neither obvious nor well-defined. We present two alternative ways of generalizing correspondence analysis, one based on the quantification of the variables and intercorrelation relationships, and the other based on the geometric ideas of simple correspondence analysis. We propose a version of multiple correspondence analysis, with adjusted principal inertias, as the method of choice for the geometric definition, since it contains simple correspondence analysis as an exact special case, which is not the situation of the standard generalizations. We also clarify the issue of supplementary point representation and the properties of joint correspondence analysis, a method that visualizes all two-way relationships between the variables. The methodology is illustrated using data on attitudes to science from the International Social Survey Program on Environment in 1993.
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- Michael Greenacre, 2008. "Correspondence analysis of raw data," Economics Working Papers 1112, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2009.
- Michael Greenacre & Rafael Pardo, 2005. "Multiple correspondence analysis of a subset of response categories," Economics Working Papers 881, Department of Economics and Business, Universitat Pompeu Fabra.
- Robert Boik, 1996. "An efficient algorithm for joint correspondence analysis," Psychometrika, Springer, vol. 61(2), pages 255-269, June.
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