The aim of this paper is to give an overview of the methodological contribution given by Italian researchers in introducing a priori information into multidimensional data analysis techniques, paying special attention to categorical variables. The basic method is Non-Symmetrical Correspondence Analysis, which enables the analysis of a contingency table when the behaviour of one variable is supposed to be dependent on the other cross-classi"ed variable. As usual correspondence analysis decomposes an association index (Pearson's ), in a principal component sense, the proposed method is based on a decomposition of a predictability index (Goodman and Kruskal's ).
Non-symmetrical correspondence analysis has been extended to more than one dependent/explanatory variable(s), by means of proper #attening procedures, i.e. by the use of multiple tables, and the decomposition of Gray and Williams' multiple and partial 's. In doing so multiple and partial versions have been proposed. A forward selection procedure for choosing the variables with higher predictive power is presented.
After a brief review of non-symmetrical correspondence analysis con"rmatory approach, the problem of validating results in terms of analytical stability and replication stability is faced by means of in#uence functions and resampling techniques.