New Developments for the Sensitivity Estimation in Four-Way Calibration with the Quadrilinear Parallel Factor Model

Appropriate closed-form expressions are known for estimating analyte sensitivities when calibrating with one-, two-, and three-way data (vectors, matrices, and three-dimensional arrays, respectively, built with data for a group of samples). In this report, sensitivities are estimated for calibration with four-way data using the quadrilinear parallel factor (PARAFAC) model, making it possible to assess important figures of merit for method comparison or optimization. The strategy is based on the computation of the uncertainty in the fitted PARAFAC parameters through the Jacobian matrix. Extensive Monte Carlo noise addition simulations in four-way data systems having widely different overlapping situations are helpful in supporting the present approach, which was also applied to two experimental analytical systems. With this proposal, the estimation of the PARAFAC sensitivity for calibration scenarios involving three- and four-way data may be considered complete.