Another look at first-order saturated designs: The p-efficient designs

The problem of constructing first-order saturated designs that are optimal in some sense has received a great deal of attention in the literature. Since these saturated designs are frequently used in screening situations, the focus will be on the potential projective models rather than the full model. This article discusses some practical concerns in choosing a design and presents some first-order saturated designs having two desirable properties, (near-) equal occurrence and (near-) orthogonality. These saturated designs are shown to be reasonably efficient for estimating the parameters of projective submodels and thus are called p-efficient designs. Comparisons with the efficiency of D-optimal designs are given for designs for all n from 3 to 30.