Stepwise orthogonalization of predictors in classification and regression techniques: An “old” technique revisited

Abstract The stepwise decorrelation of the variables, introduced by Kowalski and Bender in 1976 with the name “SELECT”, is here applied to the selection of predictors relevant both for classification and class modelling problems and for multivariate calibration (especially in the case of NIR spectroscopy). The original algorithm is modified, and it is used with a validation strategy called here “complete validation” and equipped with other diagnostics and graphic tools. The obtained models contain a minimum number of relevant predictors, and as a consequence of the stepwise decorrelation these predictors are orthogonal. So, one of the important disadvantages of the stepwise ordinary least squares regression (StepOLS) is eliminated. Moreover, SELECT can be used in problems of multivariate calibration with spectral data to identify intervals of predictors with relevant information. These predictors are very correlated, but PLS can exploit their synergism to improve the prediction ability. Stepwise orthogonalization is here applied to some data sets with attention to multivariate calibration. Results are discussed and compared with those obtained by PLS and StepOLS.