A review on second- and third-order multivariate calibration applied to chromatographic data

Analytical Figures of Merit: From Univariate to Multiway Calibration

“…20 By processing these data, considerably more complex analytical problems can be solved, [21][22][23][24][25][26][27][28][29][30][31] and predictions are even possible in the presence of unexpected spectral interferences, i.e., sample constituents not considered in the calibration phase. 32 The latter will be called, in the remainder of this paper, simply as 'unexpected interferences'.…”

“…32 Interesting experimental applications in which this advantage has been exploited for a variety of samples can be found in recent reviews. [22][23][24][25][26][27][28][29][30][31] An alternative nomenclature is based on the number of ways, which is equivalent to the number of modes of a data array for a group of samples. 32 Thus univariate and one-way calibration are synonymous, as are first-order and two-way calibration, second-order and threeway calibration, etc.…”

“…In first-order classical least-squares calibration, eq (29) naturally follows as a consequence of the LBOZ criterion, 80 by setting the denominator as equal to || s n ||, which is a measure of the pure analyte signal. However, for first-order latent based calibration models (in fact for latent models of any data order), no approximations are available to pure analyte profiles, and hence the selectivity cannot be precisely defined.…”

“…34,37,79 The defining eq (29) implies that the multi-way selectivity is accessible when the pure analyte signal is adequately retrieved by the processing algorithm. This is possible in the case of multi-linear (e.g., PARAFAC) analysis, for which the selectivity (SEL n ) is directly given by:…”

Determination of dichlobenil and its major metabolite (BAM) in onions by PTV–GC–MS using PARAFAC2 and experimental design methodology

“…PARAFAC2 model [11,12] has been shown to be very useful in determining target compounds in food commodities [13,14,15,16,17] by solving problems with co-eluting interferents, little shifts in the retention time, low signal-to-noise ratios, etc., which are usual worries to tackle in chromatographic determinations [16,15]. This three-way technique of analysis makes discrimination possible from co-eluting matrix components; this is the "second-order advantage" of the PARAFAC2 algorithm.…”