Predictive-property-ranked variable reduction with final complexity adapted models in partial least squares modeling for multiple responses.

For partial least-squares regression with one response (PLS1), many variable-reduction methods have been developed. However, only a few address the case of multiple-response partial-least-squares (PLS2) modeling. The calibration performance of PLS1 can be improved by elimination of uninformative variables. Many variable-reduction methods are based on various PLS-model-related parameters, called predictor-variable properties. Recently, an important adaptation, in which the model complexity is optimized, was introduced in these methods. This method was called Predictive-Property-Ranked Variable Reduction with Final Complexity Adapted Models, denoted as PPRVR-FCAM or simply FCAM. In this study, variable reduction for PLS2 models, using an adapted FCAM method, FCAM-PLS2, is investigated. The utility and effectiveness of four new predictor-variable properties, derived from the multiple response PLS2 regression coefficients, are studied for six data sets consisting of ultraviolet-visible (UV-vis) spectra, near-infrared (NIR) spectra, NMR spectra, and two simulated sets, one with correlated and one with uncorrelated responses. The four properties include the mean of the absolute values as well as the norm of the PLS2 regression coefficients and their significances. The four properties were found to be applicable by the FCAM-PLS2 method for variable reduction. The predictive abilities of models resulting from the four properties are similar. The norm of the PLS2 regression coefficients has the best selective abilities, low numbers of variables with an informative meaning to the responses are retained. The significance of the mean of the PLS2 regression coefficients is found to be the least-selective property.