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From correspondence analysis to multiple and joint correspondence analysis

Michael Greenacre

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

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 (search for similar items in EconPapers)
JEL-codes: C19 C88 (search for similar items in EconPapers)
Date: 2005-09
New Economics Papers: this item is included in nep-ecm
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