Theory of net analyte signal vectors in inverse regression

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Abstract
The net analyte signal and the net analyte signal vector are useful measures in building and optimizing multivariate calibration models. In this paper a theory for their use in inverse regression is developed. The theory of net analyte signal was originally derived from classical least squares in spectral calibration where the responses of all pure analytes and interferents are assumed to be known. However, in chemometrics, inverse calibration models such as partial least squares regression are more abundant and several tools for calculating the net analyte signal in inverse regression models have been proposed. These methods yield different results and most do not provide results that are in accordance with the chosen calibration model. In this paper a thorough development of a calibration‐specific net analyte signal vector is given. This definition turns out to be almost identical to the one recently suggested by Faber (Anal. Chem. 1998; 70: 5108–5110). A required correction of the net analyte signal in situations with negative predicted responses is also discussed. Copyright © 2004 John Wiley & Sons, Ltd.