D- and A-optimal Screening Designs

Abstract

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 paper 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 found through a study of their respective coordinateexchange 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 Bayesian version of the A-and D-criteria in how they 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.