Evaluation of the number of factors needed for residual bilinearization in BLLS and UPLS models to achieve the second-order advantage

Bilinear least squares (BLLS) and unfold partial least squares (UPLS) are second-order multivariate calibration methods, which require the application of the residual bilinearization (RBL) algorithm to achieve the second-order advantage. The present work presents a study of the choice of the number of RBL factors, in BLLS and UPLS models, for two different datasets based on fluorescence and flow injection analysis (FIA) measurements. Confidence limits for the noise level and mean calibration residuals, based on a student-t distribution, are proposed as a criterion for determination of the number of RBL factors. Feasible results were obtained based on the proposed confidence limits, but divergences were observed in some situations in the FIA dataset due to either differences in the models or characteristics of the analyte signal. These results suggest, whenever possible, that the number of RBL factors should be checked with a dataset composed by samples where values of the property of interest are known from a reference method.