Constrained Principal Components Analysis with External Information

In the framework of the Multidimensional Data Analysis, D'Ambra and Lauro (1982) developed "Constrained Principal Component Analysis" (CPCA) in order to study the dependence structure of a set of quantitative variables (criterion) from another set of quantitative variables (predictors). In experimental data analysis beside the variables of direct interest we often have additional information on the statistical units as well as on the explanatory variables. The analysis of the phenomena structure can be improved if we take these external information into account and a more parsimonious and easier representation of the data may be obtained. In this paper, according to the different external information, different forms of CPCA are developed.