Framework for multivariate selectivity analysis, part I: theoretical and practical merits

A number of definitions of multivariate selectivity have been proposed in the literature. Arguably, the one that enjoys the greatest chemometric attention has been the net analyte signal (NAS) based definitions of Lorber and Zinn. Recent works have suggested that similar inference can be made for inverse least-squares calibration methods (e.g., principal components regression). However, the properties of inverse calibration methods are markedly different than classical methods, so in many practical cases involving inverse models classically derived figures of merit cannot be transparently interpreted. In Part I of this work, we discuss a selectivity framework that is theoretically consistent regardless of the calibration method. Importantly, it is also experimentally measurable, either through controlled selectivity experiments, or through analysis on opportunistically acquired sample measurements. It is statistically advantageous to use the former if such control is achievable. Selectivity is defined to be a function of the change in predicted analyte concentration that will result from a change in the concentration of an interferant, an approach consistent with traditional definitions of analytical selectivity and National Committee for Clinical Laboratory Standards recommendations for interference testing. Unlike the NAS-based definition of selectivity, the definition discussed herein is relevant to only a particular analyte-interferant pair. The theoretical and experimental aspects of this approach are illustrated with simulated data herein and in Part II of this paper, which investigates several experimental near-infrared data sets.