A NOTE ON THE USE OF THE PARTIAL LEAST-SQUARES METHOD FOR MULTIVARIATE CALIBRATION

The partial least-squares (PLS) method for regression with a single analyte is, from a numerical analysis point of view, a method for obtaining a bidiagonal matrix. However, the regular formulation of PLS does not compute all quantities required for building a model and for prediction. The missing quantities are: (1) the leverage values that are important for detecting influential or outlier samples during the model building and for estimation of the number of principal components to be included in the linear model without the need for cross validation; and (2) calculation of the vector runTR+ that is required for estimating the prediction error. A modified version of the PLS method that enables the calculation of the above-mentioned quantities is presented in this note. Moreover, the modified algorithm requires less computation time and memory because there is no need to subtract the calculated factor from the data matrix at each step.