Generalized PLS regression

Abstract

Abstract The present paper develops a class of generalized partial least squares (GPLS) regression methods. GPLS can be regarded as a kind of weighted partial least squares regression method. Two special cases of them, ridge partial least squares (RPLS) and generalized ridge partial least squares (GRPLS) regression methods, are discussed in detail. RPLS and GRPLS combine partial least squares (PLS) with ridge regression (RR) and generalized ridge regression (GRR) respectively. It is shown that the estimated coefficient vectors by RPLS and GRPLS are shrunken PLS estimators and their prediction power is not so sensitive to the components included in the model compared to PLS. The four methods RR, PLS, RPLS and GRPLS are compared on the basis of three data sets under the criteria of prediction residual error sum of squares (PRESS) and mean squared error of prediction (MSEP). Copyright © 2001 John Wiley & Sons, Ltd.