Multiple analytical method comparison using maximum livelihood principal component analysis and linear regression with errors in both axes

This paper discusses a new stepwise approach for comparing the results from several analytical methods which analyse a set of analytes at different co ncentration levels, taking into account all the individual uncertainties pr oduced by measurement errors. This stepwise comparison approach detects the methods that provide outlying concentration results. The concentration res ults from each one of the remaining analytical methods are then compared to the ones from the others taken together, by using linear regression. To do this, the concentration results from the methods considered together and t heir individual uncertainties, are decomposed at each step to obtain a vect or of concentrations. This is achieved by a maximum likelihood principal co mponent analysis (MLPCA), which takes into account the measurement errors i n the concentration results. The bivariate least squares (BLS) regression m ethod is then used to regress the concentration results from the method bei ng tested at a given step on the scores generated from the MLPCA decomposit ion (which have the information of the other remaining methods), considerin g the uncertainties in both axes. To detect significant differences between the results from the method being tested at a given step and the results f rom the other methods (MLPCA scores), the joint confidence interval test is applied on the BLS regression line coefficients for a given level of signi ficance a. We have used four real data sets to provide application examples that show the suitability of the approach. (C) 2001 Elsevier Science B.V. All rights reserved.