Detection of nonlinearity in multivariate calibration

The present study categorises and compares several graphical and numerical methods to detect the presence of nonlinearity in multivariate calibration. The focus is on (quadratic) nonlinearity in the relationship between the property of interest (e.g. concentration) and the set of instrumental (e.g. absorbance) measurements. The explored techniques are applied to three simulated data sets where (non)linearity of the relationship is known, and to four experimental near infrared (NIR) data sets. Mallows augmented partial residual plot is recommended as the most universal diagnostic plot to detect nonlinearity. The significance of nonlinearity is evaluated using the runs test.