Partial least squares regression and statistical models. (English) Zbl 0713.62062

Summary: The calibration method Partial Least Squares 1 (PLS1) is described in terms of the joint covariance structure of the explanatory variables and the predicted variable. In the population version it is possible to give simple conditions for when the PLS algorithm stops after a certain number of steps, and it turns out that the resulting predictor is the same as the one given by principal component regression. The concept of relevant components is defined, and the relationship to factor analysis models is discussed. Finally, the implications for the sample version of PLS are considered, both for the case when it is used as a prediction method, and for the case when scores and loadings from PLS - in a similar way as the scores and loadings from factor analysis - are used in the interpretation of data.


62H25 Factor analysis and principal components; correspondence analysis
62J05 Linear regression; mixed models
62J99 Linear inference, regression