How to avoid over-fitting in multivariate calibration--the conventional validation approach and an alternative.

This paper critically reviews the problem of over-fitting in multivariate calibration and the conventional validation-based approach to avoid it. It proposes a randomization test that enables one to assess the statistical significance of each component that enters the model. This alternative is compared with cross-validation and independent test set validation for the calibration of a near-infrared spectral data set using partial least squares (PLS) regression. The results indicate that the alternative approach is more objective, since, unlike the validation-based approach, it does not require the use of 'soft' decision rules. The alternative approach therefore appears to be a useful addition to the chemometrician's toolbox.