Multivariate calibration models and their implementation

First-order multivariate calibration techniques and their proper implementation are described. Multivariate calibration is presented by the unified approach suggested by Sanchez and Kowalski (Sanchez,Kowalski, J. Chemometrics, 2, 247(1988)). It is shown that first-order calibration is a special case of the more general second-order calibration. Numerical techniques for solving the calibration problem as well as some alternatives to the most commonly used methods are presented.; Proper implementation of multivariate calibration is not complete without the ability to detect outlier samples which cause to bias in the model and to detect prediction samples for which the model is invalid. Various outlier detection techniques are described and the two most useful: Studentized residuals and leverage are combined into a single plot. From this kind of plot it is possible to detect both samples with unusual spectra which influence and model and samples with bad concentration values. Predicting a concentration value is not complete until it is accompanied by a number which is estimated for its uncertainty. Formulas for estimating prediction errors which take into account all possible sources of errors are derived.; From examination of the formula for prediction errors it is possible to suggest a preliminary data treatment technique which will result in lower prediction of unknown samples. The suggested preliminary data treatment replaces the conventional mean centering by centering around the expected prediction samples. Results obtained on several data sets clearly show that it is possible to achieve significant improvement.