New insights into evaluation of regression models through a decomposition of the prediction errors: application to near-infrared spectral data

Abstract

This paper analyzes the goodness of linear regression models taking into account usual criteria such as the number of principal components or latent factors, the goodness of fit or the predictive capability. Other comparison criteria, more common in an economic context, are also considered: the degree of multicollinearity and a decomposition of the mean squared error of the prediction which determines the nature, systematic or random, of the prediction errors. The applications use real data of extra-virgin oil obtained by NIR spectroscopy. The great dimensionality of the data is reduced by applying principal component analysis (PCA) and partial least squares (PLS) analysis. A possible improvement of PCA and PLS regressions by using cluster analysis or the information of the relative maxima of the spectrum is investigated. Finally, obtained results are generalized via cross-validation and bootstrapping