Multiple Co-Inertia Analysis with Linear Constraints

In several applied or theoretical fields, researchers have to deal with a lot of numerical data tables collecting different sets of variables mea- sured on the same objects or statistical units. If the collected data sets are all referred to the same variables observed in several occa- sions (different times, places, etc.) then they can be arranged into a three way data. If data are otherwise referred to different sets of variables observed on the same objects then they are considered as a multiple data set (Kiers, 1991). Several techniques for the analysis of multiple data set have been proposed (e.g. Generalized Canonical Cor- relation Analysis (Caroll,1968), Multiple Factorial Analysis (Escofier and Pages, 1984), STATIS (L’Hermier des Plantes, 1976; Lavit et al., 1994), Multiple Co-Inertia Analysis (Chessel and Hanafi, 1996)). In this paper, an extension of the Multiple Co-Inertia Analysis is proposed to take into account additional external information (as linear constraints) about the structure of the experiment. This extension is based on a objective function which takes into account directly the lin- ear constraints by rewriting the Multiple Co-Inertia Analysis objective function according to the principle of Restricted Eigenvalue Problem (Rao, 1973).