Partial least squares regression

From Wikipedia, the free encyclopedia

In statistics, the method of partial least squares regression (PLS-regression) bears some relation to principal component analysis; instead of finding the hyperplanes of maximum variance, it finds a linear model describing some predicted variables in terms of other observable variables.

It is used to find the fundamental relations between two matrices (X and Y), i.e. a latent variable approach to modeling the covariance structures in these two spaces. A PLS model will try to find the multidimensional direction in the X space that explains the maximum multidimensional variance direction in the Y space.

It was first introduced by the Swedish statistician Herman Wold. The modern (and arguably, more correct, according to Wold) long form for PLS is projection to latent structures. It is widely applied in the field of chemometrics, in sensory evaluation, and more recently, in chemical engineering process data (see John F. MacGregor) and the analysis of functional brain imaging data. Nowadays dr. J. Henseler (Radboud University Nijmegen) is the most important advocate of the PLS modeling technique. His outstanding research has contributed to a solid understanding of the practical possibilities of this exciting new method.

[edit] References

Abdi, H. "[1] (2003). Partial least squares regression (PLS-regression). In M. Lewis-Beck, A. Bryman, T. Futing (Eds): Encyclopedia for research methods for the social sciences. Thousand Oaks (CA): Sage. pp. 792-795.]".
Abdi, H. "[2] ((2007). Partial least square regression (PLS regression). In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage.".
Abdi, H. "[3] (2003). Multivariate analysis. In M. Lewis-Beck, A. Bryman, T. Futing (Eds): Encyclopedia for research methods for the social sciences. Thousand Oaks (CA): Sage. pp. 699-702.".
Frank, Ildiko and Jerome Friedman (1993). "A Statistical View of Some Chemometrics Regression Tools, Technometrics, 35(2), pp 109-148".
Henseler, Joerg and Georg Fassott (2005). "Testing Moderating Effects in PLS Path Models. An Illustration of Available Procedures, Testing Moderating Effects in PLS Path Models. An Illustration of Available Procedures".