Joint Correspondence Analysis Versus Multiple Correspondence Analysis: A Solution to an Undetected Problem

Abstract

The problem of the proper dimension of the solution of a Multiple Correspondence Analysis (MCA) is discussed, based on both the re-evaluation of the explained inertia sensu Benzécri (Les Cahiers de l’Analyse des Données 4:377–379, 1979) and Greenacre (Multiple correspondence analysis and related methods, Chapman and Hall (Kluwer), Dordrecht, 2006) and a test proposed by Ben Ammou and Saporta (Revue de Statistique Appliquée 46:21–35, 1998). This leads to the consideration of a better reconstruction of the off-diagonal sub-tables of the Burt’s table crossing the nominal characters taken into account. Thus, Greenacre (Biometrika 75:457–467, 1988) Joint Correspondence Analysis (JCA) is introduced, the results obtained on an application are shown, and the quality of reconstruction of both MCA and JCA solutions are compared to that of a series of Simple Correspondence Analyses run on the whole set of two-way tables. It results that JCA’s reduced-dimensional reconstruction is much better than the MCA’s one, that reveals highly biased and non-monotone, but also than the MCA’s re-evaluation, as suggested by Greenacre (Multiple correspondence analysis and related methods, Chapman and Hall (Kluwer), Dordrecht, 2006).KeywordsJoint Correspondence Analysis (JCA)Multiple Correspondence Analysis (MCA)GreenacreSaportaMean EigenvalueThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.