Multivariate calibration of non-replicated measurements for heteroscedastic errors

The quality of multivariate calibration (MVC) models obtained depends on the effective treatment of errors in spectral data. If errors in different absorbance measurements are correlated and have different variances, then the Maximum Likelihood Principal Component Regression (MLPCR) (Wentzell et al., Anal. Chem. 69 (1997), 2299–2311) is an optimal approach which gives a more accurate MVC model. However, this approach requires either complete knowledge of the error covariances or replicated measurements of all spectra from which an estimate of error covariances can be obtained. We propose a method for developing MVC models from non-replicated measurements when errors in different absorbances are independent, but can have different unknown variances. The core of the proposed approach is an Iterative Principal Component Analysis method which simultaneously estimates the lower dimensional spectral subspace and all the error variances. Application of this approach to simulated and experimental data sets demonstrates that the quality of the model obtained using the proposed method is better than that obtained using PCR, and is comparable to the accuracy of the model obtained using MLPCR.