Optimal two-level choice designs for any number of choice sets

Abstract

For two-level choice experiments, we obtain a simple form of the information matrix of a choice design for estimating the main effects, and provide $D$- and MS-optimal paired choice designs with distinct choice sets under the main effects model for any number of choice sets. It is shown that the optimal designs under the main effects model are also optimal under the broader main effects model. We find that optimal choice designs with a choice set size two often outperform their counterparts with larger choice set sizes.