Pls Regression and Pls Path Mod- Eling for Multiple Table Analysis

A situation where J blocks of variables are observed on the same set of individuals is considered in this paper. A factor analysis logic is applied to tables instead of individuals. The latent variables of each block should well explain their own block and in the same time the latent variables of same rank should be as positively correlated as possible. In the first part of the paper we describe the hierarchical PLS path model and remind that it allows to recover the usual multiple table analysis methods. In the second part we suppose that the number of latent variables can be different from one block to another and that these latent variables are orthogonal. PLS regression and PLS path modeling are used for this situation. This approach is illustrated by an example from sensory analysis.