From Correspondence Analysis to Multiple and Joint Correspondence Analysis

42 Pages Posted: 15 Nov 2005

See all articles by Michael Greenacre

Michael Greenacre

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

Date Written: September 1, 2005

Abstract

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.

Keywords: Correspondence analysis, eigendecomposition, joint correspondence analysis, multivariate categorical data, questionnaire data, singular value decomposition

JEL Classification: C19, C88

Suggested Citation

Greenacre, Michael John, From Correspondence Analysis to Multiple and Joint Correspondence Analysis (September 1, 2005). Available at SSRN: https://ssrn.com/abstract=847664 or http://dx.doi.org/10.2139/ssrn.847664

Michael John Greenacre (Contact Author)

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
34 93 542 25 51 (Phone)
34 93 542 17 46 (Fax)

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