Net analyte signal calculation for multivariate calibration

A unifying framework for calibration and prediction in multivariate calibration is shown based on the concept of the net analyte signal (NAS). From this perspective, the calibration step can be regarded as the calculation of a net sensitivity vector, whose length is the amount of net signal when the value of the property of interest (e.g. analyte concentration) is equal to unity. The prediction step can be interpreted as projecting a measured spectrum onto the direction of the net sensitivity vector. The length of the projected spectrum divided by the length of the net sensitivity vector is the predicted value of the property of interest. This framework, which is equivalent to the univariate calibration approach, is used for critically revising different definitions of NAS and their calculation methods. The framework is particularized for the classical least squares (CLS), principal component regression (PLS) and partial least-squares (PCR) regression models.