Local prediction models by principal component regression

Abstract

Principal component regression (PCR) is widely used for analytical calibration. In most applications of PCR, principal components (PCs) are included in regression models in sequence according to respective variances. A suitable number of PCs is determined by the predictive ability obtained through cross-validation within the calibration samples or by relying on an external validation sample set. It has recently been reported that such a strategy of selecting PCs in sequence according to variance, i.e., top-down selection, may not necessarily result in the best prediction model and some alternative strategies have been proposed. Top-down selection and other suggested selection methods aim to build a global calibration model to predict all future samples. These approaches do not take into consideration measurement information of prediction samples in forming the global model. In actuality, the best model can be different for individual prediction samples. In this paper, a strategy is proposed to build local (sample-dependent) models based on PCR. Several data sets have been investigated with up to 40% improvement in prediction errors compared to the conventional top-down selection strategy for global models.