Quantifying the Prediction Error in Analytical Multivariate Curve Resolution Studies of Multicomponent Systems

In multivariate curve resolution (MCR) analysis, a range of feasible solutions is often encountered, because of the rotational ambiguities associated with the bilinear decomposition of data matrices. For quantitative purposes, the analysis is usually applied to a carefully designed set of calibration and test samples having uncalibrated interferents. Under the usual minimal constraints (non-negativity, unimodality, species correspondence, etc.), concentration and spectral profiles of the analyte in the test samples are not univocally recovered, unlike those in the calibration samples, especially when profile overlapping with the interferents is significant and selective regions do not exist for the analyte. In this report, a quantitative measure of the prediction errors due to rotational ambiguities is discussed, based on the calculation of the differences between the maximum and minimum area under the analyte concentration profiles calculated by the MCR-BANDS procedure. This methodology can be applied in different analytical scenarios with any number of analytes and interferents. Both absolute and relative quantitative errors due to rotation ambiguities are estimated and discussed in both simulated and experimental examples derived from liquid chromatography with diode array detection. The proposed procedure can be generalized to most of the analytical situations where every instrumentally measured sample produces a data table or data matrix.