Simple Non Symmetrical Correspondence Analysis

SimpleComponentAnalysis (SCA) was introduced by Rousson and Gasser (2004) as an alternative to Principal Component Analysis (PCA). The goal of SCA is to find the “optimal simple system” of components for a given data set, which may be slightly correlated and suboptimal compared to PCA but which is easier to interpret.Aim of the present paper paper is to consider an extension of SCA to categorical data. In particular, we consider a simple version of the Non Symmetrical Correspondence Analysis (D’Ambra and Lauro, 1989). This latter approach can be seen as a centered PCA on the column profile matrix with suitable metrics enabling to describe the association in two way contingency table in cases where one categorical variable is supposed to be the explanatory variable and the other the response.