About the selection of the number of components in correspondence analysis

Abstract : Selecting the right number of axes in correspondence analysis is usually done by using empirical criteria such as :-detection of an inflexion in the diagram of eigenvalues-getting an arbitrary amount of the cumulated percentage of inertia We examine the application of a chi-square goodness of fit test between the data table and its reconstitution with k eigenvalues. This test which has been proposed by E.Malinvaud, then by E.Andersen and G.Saporta has a good behaviour for frequency tables but fails to apply to multiple correspondence analysis. This failure, however enlightens some properties of this test and of correspondence analysis.