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Partial Least Squares (PLS) Regression. Herve Abdi1

Summary: Partial Least Squares (PLS) Regression.
Herv´e Abdi1
The University of Texas at Dallas
Pls regression is a recent technique that generalizes and combines features
from principal component analysis and multiple regression. It is particularly
useful when we need to predict a set of dependent variables from a (very) large
set of independent variables (i.e., predictors). It originated in the social sciences
(specifically economy, Herman Wold 1966) but became popular first in chemo-
metrics (i.e., computational chemistry) due in part to Herman's son Svante,
(see, e.g., Geladi & Kowalski, 1986) and in sensory evaluation (Martens & Naes,
1989). But pls regression is also becoming a tool of choice in the social sciences
as a multivariate technique for non-experimental and experimental data alike
(e.g., neuroimaging, see Mcintosh, Bookstein, Haxby, & Grady, 1996). It was
first presented as an algorithm akin to the power method (used for computing
eigenvectors) but was rapidly interpreted in a statistical framework. (Frank, &
Friedman, 1993; Helland, 1990; H¨oskuldsson, 1988; Tenenhaus, 1998).
Prerequisite notions and notations
The I observations described by K dependent variables are stored in a I ×K
matrix denoted Y, the values of J predictors collected on these I observations


Source: Abdi, Hervé - School of Behavioral and Brain Sciences, University of Texas at Dallas


Collections: Biology and Medicine; Computer Technologies and Information Sciences