PLS regression methods

TLDR

Two‑block PLS is grounded in fundamental mathematical principles. The paper develops the mathematical and statistical framework of PLS regression. The authors present the PLS regression algorithm, its interpretation in model building, its statistical properties, and the decomposition structure of the data matrices.

Abstract

Abstract In this paper we develop the mathematical and statistical structure of PLS regression. We show the PLS regression algorithm and how it can be interpreted in model building. The basic mathematical principles that lie behind two block PLS are depicted. We also show the statistical aspects of the PLS method when it is used for model building. Finally we show the structure of the PLS decompositions of the data matrices involved.