Comparison of multivariate calibration methods for quantitative spectral analysis

Abstract

The quantitative prediction abilities of four multivariate calibration methods for spectral analyses are compared by using extensive Monte Carlo simulations. The calibration methods compared Include Inverse least-squares (ILS), classical least-squares (CLS), partial least-squares (PLS), and principal component regression (PCR) methods. ILS is a frequencylimited method while the latter three are capable of fullspectrum calibration. The simulations were performed assuming Beer's law holds and that spectral measurement errors and concentration errors associated with the reference method are normally distributed. Eight different factors that could affect the relative performance of the calibration methods were varied In a two-level, eight-factor experimental design In order to evaluate their effect on the prediction abilities of the four methods. It Is found that each of the three full-spectrum methods has its range of superior performance.The frequency-limited ILS method was never the best method, although In the presence of relatively large concentration errors it sometimes yields comparable analysis precision to the full-spectrum methods for the major spectral component. The Importance of each factor In the absolute and relative performances of the four methods is compared. A relatively simple model Involving the mean squared prediction errors Is developed for estimating the prediction errors for each calibration method over the range of variation of the factors considered. These results offer the analyst guidelines to be used In evaluating which multivariate calibration method will provide the best predictions when applied to a given spectral data set. In the absence of specific Information about the data set, we would recommend the use of PLS since It Is usually optimal or close to optimal.

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Partial least squares, Beer's law and the net analyte signal: statistical modeling and analysis

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