A variable elimination method to improve the parsimony of MLR models using the successive projections algorithm

The successive projections algorithm (SPA) is a variable selection technique designed to minimize collinearity problems in multiple linear regression (MLR). This paper proposes a modification to the basic SPA formulation aimed at further improving the parsimony of the resulting MLR model. For this purpose, an elimination procedure is incorporated to the algorithm in order to remove variables that do not effectively contribute towards the prediction ability of the model as indicated by an F-test. The utility of the proposed modification is illustrated in a simulation study, as well as in two application examples involving the analysis of diesel and corn samples by near-infrared (NIR) spectroscopy. The results demonstrate that the number of variables selected by SPA can be reduced without significantly compromising prediction performance. In addition, SPA is favourably compared with classic Stepwise Regression and full-spectrum PLS. A graphical user interface for SPA is available at www.ele.ita.br/kawakami/spa/.