D- and MS-optimal 2-Level Choice Designs for $N\not\equiv 0$ (mod 4)

Abstract

Street and Burgess (2007) present a comprehensive exposition of designs for choice experiments till then. Our focus is on choice experiments with two-level factors and a main effects model. We consider designs for choice experiment involving $k$ attributes (factors) and all choice sets are of size $m$. We derive a simple form of the Information matrix of a choice design for estimating the factorial effects. For $N$ being the number of choice sets in the design, we obtain $D$- and $MS$-optimal designs in the class of all designs with given $N$, $k$ and $m=2$. For given $N$ and $k$, we show that in many situations $D$-optimal designs for $m=2$ are superior than the optimal design for $m=3$ and $m=5$. Also, $MS$-optimal designs with $m=2$ are always better than the best designs under the same optimality criteria for any odd $m$. Furthermore, with respect to $trace$-optimality, there is no optimal design for $m>2$ which is better than the optimal design for $m=2$.