A Graphical Approach for Evaluating Response Surface Designs in Terms of the Mean Squared Error of Prediction

One of the fundamental purposes of response surface methodology is to develop a relatively simple linear model to explain a more complex phenomenon. Since the proposed model is only an approximation, analysts almost always must address the potential of bias due to model misspecification. This article proposes a graphical approach for evaluating response surface designs in terms of the mean squared error of prediction. In particular, this article develops measures of the maximum and minimum mean squared error of prediction over the surface of spheres through a region of interest. These measures are then plotted against radius. The resulting plots reveal at a glance how a response surface design performs in the presence of model misspecification. These plots are used to investigate the performances of several common response surface designs.