Analytical Figures of Merit for Partial Least-Squares Coupled to Residual Multilinearization

Abstract

A new expression is developed which allows estimating the sensitivity for the whole family of multivariate calibration algorithms based on partial least-squares regression combined with residual multilinearization. The sensitivity can be employed to compute other relevant figures of merit such as analytical sensitivity, limit of detection, limit of quantitation, and uncertainty in predicted concentration. The results are substantiated by extensive Monte Carlo noise addition simulations for a variety of systems with a different number of analytes and interfering agents, different degrees of overlapping in component profiles, and different numbers of instrumental data modes per sample, all requiring the achievement of the second-order advantage. The connection between the present approach and the intuitive concept of net analyte signal is discussed. An experimental example for which second-, third-, and fourth-order data are available is also studied, concerning the improvement in figures of merit on increasing the data order, which is consistent with the decrease in average prediction error.

Analytical Figures of Merit: From Univariate to Multiway Calibration

“…[40][41][42] This approach has led to the development of closed-form expressions applicable to most multi-way data processing algorithms, and has been confirmed by extensive, additive noise Monte Carlo simulations. [40][41][42] It is now possible to cast all the available sensitivity expressions into a general mathematical equation encompassing all possible degrees of data complexity, from univariate to multi-way, and in the latter case for most multi-way algorithms. Whether the general expression fits into a broader scene incorporating an intuitively useful multi-way NAS concept is probably a matter of future debate.…”

“…The scheme shown in Figure 10 can be mirrored by a Monte Carlo additive noise simulation for estimating sensitivities for any calibration model, whether univariate, multivariate or multi-way, as has been recently done. [40][41][42] This allowed operational values for the sensitivity in different calibration scenarios to be obtained, although they do not provide a closed-form sensitivity equation, which would be far more useful in this regard.…”

“…[40][41][42] The developed equations allowed to estimate the sensitivity in most of the relevant multi-way calibration models, including PARAFAC, MCR-ALS and PLS/RML, with results…”

Second- and higher-order data generation and calibration: A tutorial

“…This approach allowed to develop sensitivity expressions for multi-way 931 calibration based on PARAFAC [94], MCR-ALS [97] and PLS/RML (RML indicates 932 residual multi-linearization, and includes RBL, RTL, RQL, etc.) [98]. Further work is 933 needed, however, to validate these expressions and to include all of them into a 934 generalized conceptual scheme.…”

“…The sensitivity can be precisely calculated for three data 1004 orders: (1) second-order fixing reaction time and pH, (2) third-order fixing pH, and (3) 1005 fourth-order [98]. The result is shown in Fig.…”