Computing sensitivity and selectivity in parallel factor analysis and related multiway techniques: the need for further developments in net analyte signal theory.

Sensitivity and selectivity are important figures of merit in multiway analysis, regularly employed for comparison of the analytical performance of methods and for experimental design and planning. They are especially interesting in the second-order advantage scenario, where the latter property allows for the analysis of samples with a complex background, permitting analyte determination even in the presence of unsuspected interferences. Since no general theory exists for estimating the multiway sensitivity, Monte Carlo numerical calculations have been developed for estimating variance inflation factors, as a convenient way of assessing both sensitivity and selectivity parameters for the popular parallel factor (PARAFAC) analysis and also for related multiway techniques. When the second-order advantage is achieved, the existing expressions derived from net analyte signal theory are only able to adequately cover cases where a single analyte is calibrated using second-order instrumental data. However, they fail for certain multianalyte cases, or when third-order data are employed, calling for an extension of net analyte theory. The results have strong implications in the planning of multiway analytical experiments.