Evaluation of principal component selection methods to form a global prediction model by principal component regression

Most situations using principal component regression (PCR) as a multivariate calibration tool use the conventional top-down selection procedure to determine the number of principal components (PCs) to generate a global model, i.e., the regression model is established by including PCs in sequence according to variances related to the PCs. This model is then used to predict future samples adequately spanned by the corresponding calibration set. Recently, some alternative procedures have been proposed for PC selection with respect to multivariate calibration. These include optimization (selection) by generalized simulated annealing and correlation principal component regression (CPCR) where PCs are ordered according to correlations with the dependent variable (concentration). The PCs are then selected one by one to form the global model based on a prediction criterion. In this paper, a forward selection procedure PCR (FSPCR) is evaluated and compared to CPCR and top-down selection. Four spectroscopic data sets are analyzed for the comparison study. In essence, results reveal that PCs selected based on a top-down approach generates the most stable global model. That is, top-down selection generally performs best for prediction of numerous future samples sets compared to CPCR and FSPCR. Reasons for such differences in performances of these procedures have been analyzed.