Validation of Multivariate Calibration

The reliability of multispecies analysis has to be validated according to the usual criteria selectivity, accuracy (trueness) and precision, confidence and prediction intervals and, calculated from these, multivariate critical values and limits of detection. In multivariate calibration collinearities of variables caused by correlated concentrations in calibration samples should be avoided. Therefore, the composition of the calibration mixtures should not be varied randomly but by principles of experimental design (Deming and Morgan [1993] Morgan [1991]). 

Selectivity. In general, selectivity of analytical multicomponent systems can be expressed qualitatively (Vessman et al. [2001]) and estimated quantitatively according to a statement of Kaiser [1972] and advanced models (Danzer [2001]). In multivariate calibration, selectivity is mostly quantified by the condition number see Eqs. (6.80)-(6.82). Unfortunately, the condition number does not consider the concentrations of the species and gives therefore only an aid to orientation of maximum expectable analytical errors. Inclusion of the concentrations of calibration standards into selectivity models makes it possible to derive multivariate limits of detection. 

Precision. The uncertainty of calibration and prediction of unknown concentrations are expressed by the standard error of calibration (SEC), defined as 

Another measure for the precision of multivariate calibration is the so-called PRESS-value (predictive residual sum of squares, see Frank and Todeschini [1994]), defined as 

It can be calculated as usual for SEP, see Eq. (6.98) by use of test samples. It is also possible to estimate the PRESS-value on the basis of standard samples only applying cross validation by means of the so-called hat matrix H (Faber and Kowalski [1997a, b] Frank and Todeschini [1994])  

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