Quantifying the effect of measurement errors on the uncertainty in bilinear model predictions: a small simulation study

Four methods are compared for quantifying the effect of measurement errors on the uncertainty in bilinear model predictions. These methods amount to (1) evaluating an approximate expression for prediction variance, (2) bootstrapping residuals left after fitting the data matrices using a singular value decomposition, (3) adding noise from an appropriate distribution to the original data, and (4) jack-knifing rows and columns of the data matrices. The comparison is carried out for liquid chromatography/ultraviolet data obtained from Malinowski and the models are constructed using the generalized rank annihilation method. It is found that the first three methods give highly consistent results, whereas the jack-knife yields uncertainty estimates that have no clear interpretation.