Sample-specific standard prediction errors in three-way parallel factor analysis (PARAFAC) exploiting the second-order advantage
The calculation of sample-specific standard errors for the concentrations predicted by a three-way parallel factor analysis (PARAFAC) model exploiting the second-order advantage is discussed. A simple error propagation equation is shown to be useful for this purpose, on the condition that the correct sensitivity parameter is introduced. Two different net analyte signal definitions are tested for measures of sensitivity and are demonstrated to be applicable to different calibration scenarios, namely whether or not the second-order advantage is exploited. The results are supported by Monte Carlo calculations of variance inflation factors (including random noise only in the test sample signals) and also by experimental data concerning the determination of a therapeutic drug in human urine samples by fluorescence excitation-emission matrices. Full Monte Carlo simulations performed by adding random noise to both concentrations and instrumental signals (calibration and unknown) in several theoretical binary mixtures are in good agreement with the proposed approach. Copyright (C) 2005 John Wiley T Sons, Ltd.
sample-specific standard prediction error parallel factor analysis second-order advantage sensitivity variance inflation factor monte carlo simulations uncertainty propagation