Fraction of design space plots for examining model robustness

When choosing between competing designs, it is typical to specify a design space and model on which to base the comparison. The prediction capabilities of the design, specifically G- and V-efficiency using scaled prediction variance (SPV), are based on this chosen model. After the data are collected and individual effects are tested, some terms may not be significant in the model. In this case, the experimenter likely will decide to use a reduced model, which has only a portion of the terms included that were in the original model for which the design was chosen. This paper presents a graphical method for examining design robustness related to the SPV values using fraction of design space (FDS) plots by comparing designs across a number of potential models in a prespecified model space. The FDS plots show the various distributions of the SPV throughout the design space for different models for a chosen design on the same graph. The methods are demonstrated on several examples for different models and on a variety of design spaces.