A graphical approach for evaluating and comparing designs for nonlinear models

A graphical approach is proposed for the purpose of assessing the overall prediction capability of a nonlinear design inside a region of interest R. A visual description is given of the behavior of the mean-squared error of prediction throughout the region R. More explicitly, for each of several concentric surfaces inside R, quantile plots of the so-called estimated scaled mean-squared error of prediction (ESMSEP) are obtained. In addition, when the number of control (input) variables in the associated model is equal to one, plots of the maximum and minimum of the scaled mean-squared error of prediction (SMSEP) over a subset of the model's parameter space are developed. The latter plots are primarily used to compare several nonlinear designs. Two examples are presented to demonstrate the usefulness of the proposed plots.