Multiple factor analysis for contingency tables in the FactoMineR package

Abstract

We present multiple factor analysis for contingency tables (MFACT) and its implementation in the FactoMineR package. This method, through an option of the MFA function, allows us to deal with multiple contingency or frequency tables, in addition to the categorical and quantitative multiple tables already considered in previous versions of the package. Thanks to this revised function, either a multiple contingency table or a mixed multiple table integrating quantitative, categorical and frequency data can be tackled. The FactoMineR package (Lê et al., 2008; Husson et al., 2011) offers the most commonly used principal component methods: principal component analysis (PCA), correspondence analysis (CA; Benzécri, 1973), multiple correspondence analysis (MCA; Lebart et al., 2006) and multiple factor analysis (MFA; Escofier and Pagès, 2008). Detailed presentations of these methods enriched by numerous examples can be consulted at the website http://factominer.free.fr/. An extension of the MFA function that considers contingency or frequency tables as proposed by Bécue-Bertaut and Pagès (2004, 2008) is detailed in this article. First, an example is presented in order to motivate the approach. Next, the mortality data used to illustrate the method are introduced. Then we briefly describe multiple factor analysis (MFA) and present the principles of its extension to contingency tables. A real example on mortality data illustrates the handling of the MFA function to analyse these multiple tables and, finally, conclusions are presented.