Application of Maximum Likelihood Principal Components Regression to Fluorescence Emission Spectra

Abstract

The application of maximum likelihood multivariate calibration methods to the fluorescence emission spectra of mixtures of acenaphthylene, naphthalene, and phenanthrene in acetonitrile is described. Maximum likelihood principal components regression (MLPCR) takes into account the measurement error structure in the spectral data in constructing the calibration model. Measurement errors for the fluorescence spectra are shown to exhibit both a heteroscedastic and correlated noise structure. MLPCR is compared with principal components regression (PCR) and partial least-squares regression (PLS). The application of MLPCR reduces the prediction errors by about a factor of two over PCR and PLS when a pooled estimate of the measurement error covariance matrix is employed. However, when only the heteroscedascity is incorporated into MLPCR, no improvement in results is observed, indicating the importance of accounting for correlated measurement errors.