PLS works

Abstract

In a recent paper, claims were made that most current implementations of PLS provide wrong and misleading residuals [1]. In this paper the relation between PLS and Lanczos bidiagonalization is described and it is shown that there is a good rationale behind current implementations of PLS. Most importantly, the residuals determined in current implementations of PLS are independent of the scores used for predicting the dependent variable(s). Oppositely, in the newly suggested approach, the residuals are correlated to the scores and hence may be high due to variation that is actually used for predicting. It is concluded that the current practice of calculating residuals be maintained. Copyright © 2008 John Wiley & Sons, Ltd.