Second-order multivariate calibration with the extended bilinear model: Effect of initialization, constraints, and composition of the calibration set on the extent of rotational ambiguity

Abstract

Extended bilinear modeling is popular in second-order multivariate calibration, particularly when the matrix data for each sample are of chromatographic origin. Since elution time profiles vary across samples, in both shape and peak position, it is not possible to process these data in a three-way trilinear format. In these cases, the most successful model for quantitating analytes in the presence of interferents is multivariate curve resolution-alternating least squares (MCR-ALS) in its extended version, ie, processing an augmented data matrix built with the matrices for a test sample and the calibration samples, appended in the direction of the elution time mode. MCR-ALS starts with certain initial profiles and applies a set of natural constraints during the ALS phase, whose purpose is to reduce the range of feasible solutions or to lead to unique bilinear solutions if possible. In this report, a simulated second-order three-component system (two calibrated analytes and one uncalibrated interferent in test samples) is studied regarding the presence of rotational ambiguity in the bilinear solutions, using (a) a grid search methodology to compute the feasible solutions and (b) MCR-ALS on a large set of test samples to estimate the average prediction errors. Various initialization schemes and constraints are probed, and the results are compared in terms of the extent of rotational ambiguity and global uncertainty in predicted concentrations.