Compound optimality criteria and graphical tools for designs for prediction

The prediction capability of a design is an important issue in response surface methodology. Following the line of argument that a design should have several desirable properties, we have extended an existing compound design criterion to include prediction properties, with interval predictions allowed for. We explain that predictions of differences in responses are often more useful than predictions of responses themselves, which leads to the definition of the (IDP)$(I_DP)$-optimality criterion. The work also introduces several extensions of existing graphical tools for inspecting prediction performances of the designs in the whole region of experimentation. Two examples illustrate the methods, one for the cubic and the other for the spherical region. We compare the new, classical and standard optimum designs using the graphical tools.