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

Authors
Harald Martens and Magni Martens
Published
2000
DOI
10.1016/S0950-3293(99)00039-7
Citation
Martens and Martens: "Modified jack-knife estimation of parameter uncertainty in bilinear modelling by partial least squares regression (PLSR)", Food Quality and Preference, 11, 5-16, 2000.
Abstract
A method for assessing the uncertainty of the individual bilinear model parameters from two-block 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.
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