Optimal two-level choice designs for estimating main effects and specified two-factor interactions

Abstract

Over two decades, optimal choice designs have been obtained for estimating the main effects and the main plus two-factor interaction effects under both the multinomial logit model and the linear paired comparison model. However, there are no general results on the optimal choice designs for estimating main plus {\it some} two-factor interaction effects. We consider a model involving the main plus two-factor interaction effects with our interest lying in the estimation of the main effects and a specified set of two-factor interaction effects. The specified set of the two-factor interaction effects include the interactions where only one of the factors possibly interact with the other factors. We first characterize the information matrix and then construct universally optimal choice designs for choice set sizes 3 and 4.