Analytical Figures of Merit in Univariate, Multivariate, and Multiway Calibration: What Have We Learned? What Do We Still Need to Learn?

An overview of the status of the research in analytical figures of merit is provided, including all calibration scenarios from univariate to multivariate and multiway analytical protocols. Both linear and nonlinear multivariate models are considered. Starting with the simplest multivariate model, inverse least-squares regression, the basic concepts of sensitivity, sample leverage, and limit of detection are introduced. The extension to other multivariate models is discussed, as well as to nonlinear models based on radial basis functions, kernel partial least-squares, and multilayer feed-forward artificial neural networks. Finally, multiway calibration models are discussed, including multilinear decomposition models such as parallel factor analysis (PARAFAC) and multivariate curve resolution–alternating least-squares (MCR-ALS). In the latter case, recent developments concerning the pervasive phenomenon of rotational ambiguity are discussed. Unfinished works and areas where further research efforts are needed to develop closed-form expressions and to fully understand their meaning are included.