Multivariate curve resolution-alternating least-squares and second-order advantage in first-order calibration. A systematic characterisation for three-component analytical systems

Abstract

Background: Recent interest has been focused on the application of multivariate curve resolution-alternatingleast-squares (MCR-ALS) to systems involving the measurement of first-order and non-bilinear second-orderdata. The latter pose important challenges to bilinear decomposition models, due to the phenomenon of rotationalambiguity in the solutions, even under the application of the full set of chemical constraints that is usuallyemployed in MCR-ALS calibration.Results: After the analysis of several simulated and experimental datasets, important conclusions regarding therole of the selectivity patterns in the constituent spectra have been drawn concerning the achievement of the second-order advantage. Theoretical considerations based on the calculation of the areas of feasible solutionshelped to support the observations regarding the predictive ability of MCR- ALS in the various datasets.Significance: The understanding of the impact of rotational ambiguity in obtaining the second-order advantagewith both first-order and non-bilinear second-order data is of paramount importance in the future developmentof analytical protocols of complex samples.