Three-Dimensional Quantile Plots and Dynamic Quantile Plots of the Prediction Variance for Response Surface Designs

摘要

A historically common choice for evaluating response surface designs is to use alphabetic optimality criteria. Single-number criteria such as D, A, G, and V optimality do not completely reflect the estimation or prediction variance characteristics of the designs in question. For prediction-based assessment, alternatives to single-number summaries include the graphical displays of the prediction variance across the design regions. Variance dispersion graphs, fraction of design space plots, and quantile plots have been suggested to evaluate the overall prediction capability of response surface designs. The quantile plots use the percentiles. These quantile plots use the percentiles of the distribution at a given radius instead of just the mean, maximum, and minimum prediction variance values on concentric spheres inside the region of the interest. Previously, the user had to select several values of radius and draw corresponding quantile plots to evaluate the overall prediction capability of response surface designs. The user-specified choice of radii to examine makes the plot somewhat subjective. Alternately, we propose to remove this subjectivity by using a three-dimensional quantile plot. As another extension of the quantile plots, we suggest dynamic quantile plots to animate the quantile plots and use them for comparing and evaluating response surface designs.