New Prediction-Augmented Classical Least-Squares (PACLS) Methods: Application to Unmodeled Interferents

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Abstract
A significant improvement to the classical least-squares (CLS) multivariate analysis method has been developed. The new method, called prediction-augmented classical least-squares (PACLS), removes the restriction for CLS that all interfering spectral species must be known and their concentrations included during the calibration. We demonstrate that PACLS can correct inadequate CLS models if spectral components left out of the calibration can be identified and if their “spectral shapes” can be derived and added during a PACLS prediction step. The new PACLS method is demonstrated for a system of dilute aqueous solutions containing urea, creatinine, and NaCl analytes with and without temperature variations. We demonstrate that if CLS calibrations are performed with only a single analyte's concentrations, then there is little, if any, prediction ability. However, if pure-component spectra of analytes left out of the calibration are independently obtained and added during PACLS prediction, then the CLS prediction ability is corrected and predictions become comparable to that of a CLS calibration that contains all analyte concentrations. It is also demonstrated that constant-temperature CLS models can be used to predict variable-temperature data by employing the PACLS method augmented by the spectral shape of a temperature change of the water solvent. In this case, PACLS can also be used to predict sample temperature with a standard error of prediction of 0.07 °C even though the calibration data did not contain temperature variations. The PACLS method is also shown to be capable of modeling system drift to maintain a calibration in the presence of spectrometer drift.