Explanatory methods for comparative analyses

The aim of the paper is to give some insights into the different methods for the simultaneous and comparative analysis of particularly structured multiple matrices. These matrices are made up of multivariate multi-occasion data. These data relate to several variables collected on the same set of statistical units and under different observational conditions. The paper is set in a nonsymmetrical framework where external, usually condition-invariant, information on the variablesʹ dependence structure is taken into account. Therefore, the paper proposes some extensions of the method called principal component analysis onto a reference subspace (PCAR) to the case of more than one response data sets. Finally, where they exist, the links between these methods and partial least squares (PLS) regression are presented. The geometrical aspects of such methods as well as their interpretative tools, useful in new specific fields of application, are the main focus of the paper.