Non symmetrical multiple correspondence analysis with linear constraints.

In the framework of the Multidimensional Data Analysis, Lauro and D’Ambra (1984) developed "Non Symmetrical Multiple Correspondence Analysis" (NSMCA) in order to study the dependence structure of a qualitative variable (criterion) from two or more qualitative variables (predictors) codified in a complete disjunctive form. From a geometrical point of view, NSMCA aims at finding out the best approximation of the categories of the criterion variable into the vectorial subspaces spanned by the categories of the explanatory variables taking into account the orthogonal decomposition: global inertia = explained inertia + residual inertia. In this paper, according to a further decomposition of the global inertia, an extension of NSMCA, which considers linear constraints, is developed.