Comparison of the single channel and multichannel (multivariate) concepts of selectivity in analytical chemistry

Different measures of selectivity are in use for single channel and multichannel linear analytical measurements, respectively. It is important to understand that these two measures express related but still distinctly different features of the respective measurements. These relationships are clarified by introducing new arguments. The most widely used selectivity measure of multichannel linear methods (which is based on the net analyte signal, NAS, concept) expresses the sensitivity to random errors of a determination where all bias from interferents is computationally eliminated using pure component spectra. The conventional selectivity measure of single channel linear measurements, on the other hand, helps to estimate the bias caused by an interferent in a biased measurement. In single channel methods expert knowledge about the samples is used to limit the possible range of interferent concentrations. The same kind of expert knowledge allows improved (lower mean squared error, MSE) analyte determinations also in "classical" multichannel measurements if those are intractable due to perfect collinearity or to high noise inflation. To achieve this goal bias variance tradeoff is employed, hence there remains some bias in the results and therefore the concept of single channel selectivity can be extended in a natural way to multichannel measurements. This extended definition and the resulting selectivity measure can also be applied to the so-called inverse multivariate methods like partial least squares regression (PLSR), principal component regression (PCR) and ridge regression (RR).