PLS regression, PLS path modeling and generalized Procustean analysis: a combined approach for multiblock analysis

V. Esposito Vinzi, M. TENENHAUS

Journal of Chemometrics

March 2005, vol. 19, n°3, pp.145-153

Departments: Economics & Decision Sciences

Keywords: Multiblock analysis, PLS regression, PLS path modeling, Generalized canonical correlation analysis, Generalized Procrustean 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 variables. The latent variables of each block should well explain their own block and, at the same time, the latent variables of same order should be as positively correlated as possible to improve interpretation. The paper first (1) reviews the main methods for multiblock analysis based on a criterion to be optimized, (2) describes the hierarchical PLS path modeling algorithm and (3) recalls that it allows one to recover some usual multiblock analysis methods. It is then supposed 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. The relation between Horst's generalized canonical correlation analysis and generalized Procrustean analysis for this specific application is also studied. The approach is illustrated by an example from sensory analysis