Improved variable selection procedure for multivariate linear regression

This paper reports the development of an improved variable selection procedure for Multivariate Linear Regression (MLR). The procedure has been compared to the more commonly applied techniques of Principle Component Regression (PCR) and Partial Least Squares Regression (PLS) and was found to outperform both techniques in terms of prediction ability of a previously unseen sample when tested using three data sets (two UV and one FT–IR data set). The technique described will illustrate that many of the shortcomings of the MLR method can be overcome by optimizing the selection of variables specifically for prediction, rather than the ability to model the training data. The paper also demonstrates that a very small calibration set consisting of the pure components only can be used to produce a good model for prediction. The procedure is iterative, and as such there are many possible combinations of variables which can be found, this paper will demonstrate that the approach will reach an optimum quickly, and give a stable answer even if the training time is short. The procedure is however more computationally time consuming than PCR and PLS but as data collection is by far the most time consuming aspect, it is not considered to be a serious problem.