QB-optimal two-level designs for the baseline parameterization

Abstract

There has been recent interest in the baseline parameterization for two-level factorial designs. The association matrix that expresses the estimator of effects under the baseline parameterization is obtained in an equivalent form as a linear function of estimators of effects under the traditional centered parameterization. This allows the generalization of the $Q_B$ criterion which evaluates designs under model uncertainty in the traditional centered parameterization to be applicable to the baseline parameterization. Some optimal designs under the baseline parameterization seen in the previous literature are evaluated and it has been shown that at a given prior probability of a main effect being in the best fitted model from the experimental data, the design in the literature converges to being $Q_B$ optimal as the probability of an interaction being in that model converges to 0 from above. The $Q_B$ optimal designs for two setups of factors and run sizes at various priors are found by an extended coordinate exchange algorithm and the evaluation of their performances are discussed. Comparisons have been made to those optimal designs restricted to be level-balanced and orthogonal.