Second-order and higher-order multivariate calibration methods applied to non-multilinear data using different algorithms

We discuss and evaluate the current state of second-order and higher-order multivariate calibration methods devoted to the determination of compounds in non-multilinear data systems. We examine possible causes of multilinearity deviations:(1)a non-linear relationship between signal and analyte concentration;(2)a signal for a given sample that is non-multilinear; and,(3)component profiles that are not constant across the different samples.We discuss the advantages and the limitations of the algorithms available to cope with these different situations.The review covers relevant analytical problems found in samples of environmental and biological interest, highlighting some significant examples, and evaluating the advantages and the limitations of the different algorithms available.