Contributions to the problem of approximation of non-linear data with linear PLS in an absorption spectroscopic context

This paper presents a simple way to extend the regressor variables in PLS. The method is particularly suited for non-linear absorption spectra or any other measurements of soft saturation type. Absorption below a certain limit is described as linear and above this limit as non-linear. The extension of the regressor variables are the squared absorbances above the linear range. The proposed method is compared with both PLS and with PLS where regressors are extended with the squared X-block. The proposed method gives more parsimonious models and better predictions than existing methods for the data set used in this study, UV–VIS with absorbances in the region 0–2.8.