On a versatile second‐order multivariate calibration method based on partial least‐squares and residual bilinearization: Second‐order advantage and precision properties

Abstract

AbstractThe successful combination of unfolded partial least‐squares (U‐PLS) and residual bilinearization (RBL) constitutes a second‐order multivariate calibration method capable of achieving the second‐order advantage. RBL is performed by varying the test sample scores in order to minimize the residues of a combined U‐PLS/singular value decomposition model (SVD), using a Gauss–Newton (GN) procedure. The sample scores are then employed to predict the analyte concentration, with regression coefficients taken from the calibration step. The technique is able to handle calibration information when only certain analyte concentrations or reference properties are known, as is customary for PLS models. It has been successfully applied to model systems showing linear dependency due to pH equilibria or reaction kinetics, and experimental data aimed at the quantitation of analytes in complex samples. The predictive ability has been compared to those of parallel factor analysis and bilinear least‐squares (BLLS). The precision properties of the U‐PLS/GN‐RBL model have been investigated with the aid of Monte Carlo noise addition, and also by a new theoretical approach to sensitivity calculations. The results show good agreement between theory and simulations, and indicate that the precision and sensitivity of the U‐PLS/GN‐RBL method are comparable to other second‐order multivariate algorithms. Copyright © 2005 John Wiley & Sons, Ltd.