D- and A-Optimal Screening Designs

In practice, optimal screening designs for arbitrary run sizes are traditionally generated using the D-criterion with factor settings fixed at ±1, even when considering continuous factors with levels in [−1,1]. This article identifies cases of undesirable estimation variance properties for such D-optimal designs and argues that generally A-optimal designs tend to push variances closer to their minimum possible value. New insights about the behavior of the criteria are gained through a study of their respective coordinate-exchange formulas. The study confirms the existence of D-optimal designs comprised only of settings ±1 for both main effect and interaction models for blocked and unblocked experiments. Scenarios are also identified for which arbitrary manipulation of a coordinate between [−1,1] leads to infinitely many D-optimal designs each having different variance properties. For the same conditions, the A-criterion is shown to have a unique optimal coordinate value for improvement. We also compare how Bayesian versions of the A- and D-criteria balance minimization of estimation variance and bias. Multiple examples of screening designs are considered for various models under Bayesian and non-Bayesian versions of the A- and D-criteria.