Experimental design applied to the selection of samples and sensors in multivariate calibration

Identifier:  TDX:798

Handle: https://hdl.handle.net/20.500.11797/TDX798

Authors:  Ferré Baldrich, Joan

Abstract:
Multivariate calibration models relate instrumental responses (e.g. spectra) of a set of calibration samples to the quantities of chemical or physical variables such as analyte concentrations, or indexes (e.g. octane number in fuels). This relationship is used to predict these quantities from the instrumental response data of new unknown samples measured in the same manner. <br/><br/>Prediction using multivariate calibration models is becoming one common step in the analytical procedure. Therefore, the ability of the model to give precise and unbiased predictions has a decisive influence on the quality of the analytical result. It is important that the calibration samples and sensors be carefully selected so that the models can properly represent the phenomenon under study and assure the quality of the predictions.<br/><br/>We have studied the selection of calibration samples from the list of all the available samples in principal component regression (PCR) and the selection of wavelengths in classical least squares (CLS). The underlying basis has been given by experimental design theory. <br/><br/>In PCR, the minimum number of calibration samples are selected using the instrumental responses of the candidate samples. The analyte concentration is only determined in the selected samples. Different uses of the D-criterion have also been proposed.<br/><br/>In CLS, different criteria for wavelength selection have been interpreted from the point of view of the experimental design using the confidence hyperellipsoid of the predicted concentrations. The criteria have also been critically reviewed according to their effect on precision, accuracy and trueness (which are revised following ISO definitions). Based on the experimental design theory, new guidelines for sensor selection have been given. Moreover, a new method for detecting and reducing bias in unknown samples to be analyzed using CLS.<br/><br/>Conclusions<br/>1. Optimality criteria derived from experimental design in MLR have been applied to select calibration wavelengths in CLS and the minimum number of calibration samples in MLR and PCR from the instrumental responses or principal component scores of a list of candidates. These criteria are an alternative (and/or a complement) to the experimenter's subjective criterion. The models built with the points selected with the proposed criteria had a smaller variance of the coefficients or concentrations and better predictive ability than the models built with the samples selected randomly <br/> <br/>2. The D-criterion has been successfully used for selecting calibration samples in PCR and MLR, for selecting a reduced set of samples to assess the validity of PCR models before standardization and for selecting wavelengths in CLS from the matrix of sensitivities. D optimal calibration samples generally give PCR and MLR models with a better predictive ability than calibration samples selected randomly or using the Kennard-Stone algorithm.<br/> <br/>3. Optimization algorithms are needed to find the optimal subsets of I points from a list of N candidates. Fedorov's algorithm, Kennard-Stone algorithm and Genetic Algorithms were studied here. <br/> <br/>4. The confidence ellipsoid of the estimated concentrations and the experimental design theory provide the framework for interpreting the effect of the sensors selected with these criteria on the prediction results of the model and for deriving new guidelines for wavelength selection. <br/> <br/>5. The efficacy of the selection criteria in CLS based on the calibration matrix requires there to be no bias in the response at the selected sensors. The quality of the data must be checked before a wavelength selection method is used.<br/> <br/>6. The net analyte signal (NAS) is important to understand the quantification process in CLS and the propagation of errors to the predicted concentrations. Diagnostics such as sensitivity, selectivity and net analyte signal regression plots (NASRP) which are based on the NAS for each particular analyte have been used. The norm of the NAS has been found to be related to the prediction error .<br/> <br/>7. The NASRP is a tool for graphically detecting whether the measured response of the unknown sample follows the calculated model. The estimated concentration is the slope of the straight line fitted to the points in this plot. The sensors with bias can be detected and the sensors that best follow the model can be selected using the Error Indicator function and a moving window method.