Mean centering and computation of scalar net analyte signal in multivariate calibration

Abstract

Lorber has identified the net analyte signal (NAS) vector as the part of the gross signal which is orthogonal to the pure spectra of the interferents. For calculation of multivariate analytical figures of merit, such as sensitivity and signal-to-noise ratio, the NAS vector must be converted into a scalar NAS. The traditional methods for calculating the scalar NAS amount to taking the Euclidean norm of the NAS vector. For mean-centered data, straightforward implementation of this recipe leads to an artifact: one value for the scalar NAS corresponds to two values for analyte concentration, i.e. the conversion is not unique. This paper details the origin of the problem and proposes a simple solution. The improved calculation of scalar NAS is illustrated on the near-infrared prediction of weight per cent oxygen delivered by the oxygenate methyl tert-butyl ether in standard reference material gasoline ampoules. Copyright © 1998 John Wiley & Sons, Ltd.