$Q_B$ Optimal Two-Level Designs for the Baseline Parameterization

TL;DR

This paper extends the $Q_B$ criterion to baseline parameterization, evaluates existing designs, and finds new $Q_B$ optimal designs for two-factor setups using an extended coordinate exchange algorithm.

Contribution

It generalizes the $Q_B$ criterion to baseline parameterization and develops new optimal designs using an extended coordinate exchange algorithm.

Findings

Optimal designs converge to $Q_B$ optimality as interaction probability decreases.

Evaluated existing baseline designs and compared their performance.

Developed $Q_B$ optimal designs for various factor and run size setups.

Abstract

We have established the association matrix that expresses the estimator of effects under baseline parameterization, which has been considered in some recent literature, in an equivalent form as a linear combination 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 model, the design converges to $Q_B$ optimal as the probability of an interaction being in the best 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 level balance and orthogonality conditions.