Second-order bilinear calibration : the effects of vectorising the data matrices of the calibration set

In a groundbreaking paper, Linder and Sundberg [Chemometr. Intell. Lab. Syst. 42 (1998) 159] developed a statistical framework for the calibration of second-order bilinear data. Within this framework, they formulated three different predictor construction methods [J. Chemom. 16 (2002) 12], namely the so-called naïve method, the bilinear least squares (BLLS) method, and a refined version of the latter that takes account of the calibration uncertainty. Elsewhere [J. Chemom. 15 (2001) 743], a close relationship is established between the naïve method and the generalized rank annihilation method (GRAM) by comparing expressions for prediction variance. Here it is proved that the BLLS method can be interpreted to work with vectorised data matrices, which establishes an algebraic relationship with so-called unfold partial least squares (PLS) and unfold principal component regression (PCR). It is detailed how these results enable quantifying the effects of vectorising bilinear second-order data matrices on analytical figures of merit and variance inflation factors

Quantifying selectivity in spectrophotometric multicomponent analysis

According to the latest recommendation of the International Union of Pure and Applied Chemistry, "selectivity refers to the extent to which the method can be used to determine particular analytes in mixtures or matrices without interferences from other components of similar behavior". Because of the prime importance of selectivity as an analytical figure of merit, numerous proposals have been published on how to quantify it in spectrophotometric multicomponent analysis. We show that the criterion independently developed by Lorber [11,12] and Bergmann, von Oepen and Zinn [13] is the most suitable, because it directly relates to prediction uncertainty and allows for a consistent generalization to more complex systems of chemical analysi