Comments on “interrelationships between sensitivity and selectivity measures for spectroscopic analysis”

In a recent paper Kalivas and Lang state that Lorberʹs multivariate sensitivity only relates to the unscaled variance inflation factor if the number of calibration samples equals the number of analytes i.e. if pure-component spectra are used to form the response matrix. This paper gives a proof that Lorberʹs multivariate sensitivity obeys the desired relationship under the general conditions implied by a good calibration design. Emphasis is placed on making a clear distinction between expected (true), observed (measured) and estimated quantities. This facilitates the discussion of the practical evaluation of the defining equations and thereby solves some problems that are present in the original work. The alternative definition for multivariate sensitivity proposed by Kalivas and Lang is also discussed.