Qualitative Information from Multivariate Calibration Models

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Abstract
Multivariate calibration methods are implicit modeling methods as opposed to explicit methods that impose a theoretical model on the experimental data. Because these methods incorporate variance in the data not necessarily related to the property of interest, implicit models should be both quantitatively and qualitatively validated. Qualitative validation using the regression vector is discussed here. When the regression vector found by calibration is multiplied by the response vector of an unknown sample, it gives an estimate of the property of interest. When used with spectroscopy, the regression vector contains information about the pure spectrum of the analyte of interest, but ambiguities exist because of mathematical constraints that hinder direct extraction of this information. Results from simulated data show that, if the measured data are all positive, the presence of negative regions in the regression vector indicates overlap between the pure spectra of the analyte of interest and the interferent(s), and the qualitative information is limited. Transformations using derivatives are presented that help remove some of the ambiguity. For two-component linear systems, the derivative of the pure spectrum of the interferent component can be calculated. With multicomponent systems, derivative transformations locate some peak maxima in the pure spectra of the interferent components.