Analytical figures of merit for partial least-squares coupled to residual multilinearization

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.