Alternative interpretations to the non symmetrical correspondence analysis

In the study of the modelling relationships between dependent variables and other explanatory variables we find linear combinations called latent variables, which been obtained by means of several different methods. The goal is to model the predictive relationships between a response variable set and predicting variable set. The study of predictions could be dealt with by means of several approaches: 1) Constraint Principal Component Analysis (D’Ambra, Lauro, 1982; CPCA); 2) Canonical Analysis (Hotelling, 1933). These approaches consist of determining two subspaces of orthogonal latent variables, for the response and explicative variables, respectively. When there are collinearity problems, these approaches cannot be used. The principal purpose of this paper is to present different interpretations to the Non Symmetrical Correspondence Analysis (Lauro, D’Ambra, 1984; NSCA) using Partial Least Squares (Wold, 1966; PLS) approaches. We show that NSCA can be obtained by regression analysis and the results can be extended to the variants of the NSCA.