Modified Jack-knife estimation of parameter uncertainty in bilinear modelling by partial least squares regression (PLSR)

A method for assessing the uncertainty of the individual bilinear model parameters from twoblock regression modelling by multivariate partial least squares regression (PLSR) is presented. The method is based on the so-called "Jack-knife" resampling, comparing the perturbed model parameter estimates from cross-validation with the estimates from the full model. The conventional jack-knifing from ordinary least squares regression is modified in order to compensate for rotational ambiguities of bilinear modelling. The method is intended to make "do-it-yourself" multivariate data-analysis by non-statisticians more safe, in particular in cases with many collinear and noisy regressor and -regressand variables (which is very common in practice). Its use is illustrated by a real example, where the chemical and physical properties of different cocoa drinks are predicted from sensory analysis.