Maximum likelihood unfolded principal component regression with residual bilinearization (MLU-PCR/RBL) for second-order multivariate calibration

•New second order calibration model applying maximum likelihood strategy.•Incorporation of the noise information in both calibration and RBL phases.•Evaluation in simulated data in distinct overlap conditions, noise types and levels.•Experimental results for simultaneous determinations in pharmaceutical products.•Prediction improvement in both simulated and experimental data.

A maximum likelihood model is described for performing second-order multivariate calibration with unfolded principal component regression with residual bilinearization (MLU-PCR/RBL). It differs from the conventional RBL models based on U-PCR or U-PLS (unfolded partial least-squares) in the incorporation of the measurement error information into both the U-PCR calibration and the RBL model phases. The error information is represented by the instrumental error covariance matrix. Simulations were made by adding correlated and proportional noise to synthetic systems consisting of one analyte in the presence of a calibrated and unexpected interferent, under different conditions of overlapping profiles, noise levels and noise types (correlated and proportional). The results show that MLU-PCR/RBL outperforms conventional RBL methods in prediction ability, as confirmed by a detailed study on validation samples through the average prediction error as a convenient figure of merit. Results obtained in experimental data set based on flow injection analysis and UV detection for determination of acetylsalicylic and ascorbic acids in pharmaceutical products also support the theoretical conclusions.