Interactive variable selection (IVS) for PLS. Part II: Chemical applications

Abstract

With the aim of developing PLS models with improved predictive properties, an interactive variable selection (IVS) approach for PLS regression was introduced in Part I of this series. IVS-PLS is based on a dimension-wise selective removal of single elements in the PLS weight vector w. IVS uses cross-validation (CV) as a guiding tool. The present paper illustrates the use of IVS-PLS on both simulated data and real examples from chemistry. In the first example, spectrophotometric data were simulated according to an experimental design. The objective was to see how IVS-PLS was influenced by different levels of noise in X and Y and by the number of predictor variables (K). The results of the modelling are shown as response surfaces. In addition, four real examples were modelled by the IVS-PLS technique. The real data sets were chosen to reflect different types of data from chemistry. For each example a comparison of ‘prediction error sum of squares’ (PRESS) between IVS-PLS and classical PLS is made

For most of the examples containing many predictor variables IVS-PLS shows an improvement in predictive properties over classical PLS. Also, improvements for IVS-PLS2 (modelling of more than one y-variable) models were found. For data sets with a moderate number of variables the influence of the IVS method becomes less pronounced.