Principal component regression (PCR) and partial least squares regression (PLSR)

Ordinary least squares regression is summarized, with emphasis on the variance problem caused by collinear predictor variables. A theoretical and optimal estimation solution to this problem is presented and the relations to Kalman filtering as well as to principal component regression (PCR) and partial least squares regression (PLSR) are pointed out. The theory behind PCR and PLSR is given, and alternative PLSR models and their different residuals are compared. The PLSR residual issue in process monitoring is discussed in some detail. PLSR score-loading correspondence is discussed, and PCR and PLSR model reduction methods are presented and discussed. Established PCR and PLSR practices are summarized, with reference to the literature; finally, some emerging methods in food science are mentioned.