Evaluation of trends in residuals of multivariate calibration models by permutation test

Abstract This paper proposes the use of a nonparametric permutation test to assess the presence of trends in the residuals of multivariate calibration models. The permutation test was applied to the residuals of models generated by principal component regression (PCR), partial least squares (PLS) regression and support vector regression (SVR). Three datasets of real cases were studied: the first dataset consisted of near-infrared spectra for animal fat biodiesel determination in binary blends, the second one consisted of attenuated total reflectance infrared spectra (ATR-FTIR) for the determination of kinematic viscosity in petroleum and the third one consisted of near infrared spectra for the determination of the flash point in diesel oil from an in-line blending optimizer system of a petroleum refinery. In all datasets, the residuals of the linear models presented trends that have been satisfactorily diagnosed by a permutation test. Additionally, it was verified that 500,000 permutations were enough to produce reliable test results.