Comparison of principal components regression and partial least squares regression through generic simulations of complex mixtures

Two of the most widely employed multivariate calibration methods, principal components regression (PCR) and partial least squares regression (PLS), are compared using simulation studies of complex chemical mixtures which contain a large number of components. Details of the complex mixture model, including concentration distributions and spectral characteristics, are presented. Results from the application of PCR and PLS are presented, showing how the prediction errors and number of latent variables (NLV) used vary with the relative abundance of mixture components. Simulation parameters varied include the distribution of mean concentrations, spectral correlation, noise level, number of mixture components, number of calibration samples, and the maximum number of latent variables available. In all cases, except when artificial constraints were placed on the number of latent variables retained, no significant differences were reported in the prediction errors reported by PCR and PLS. PLS almost always required fewer latent variables than PCR, but this did not appear to influence predictive ability.