Efficiency of the coordinate-exchange algorithm in constructing exact optimal discrete choice experiments

Abstract

The use of discrete choice experiments (DCEs) for modeling real marketplace choices, in both fundamental and applied research, has gained much attention recently. To improve the quality of designing DCEs, most researchers have drawn on optimal design theory. Because of the nonlinearity of the probabilistic choice models, to construct a proper choice design, one needs the help of efficient search algorithms, among which the coordinate-exchange algorithm (CEA) has shown itself to work very well under the widely used multinomial logit discrete choice model. However, due to the discrete nature of the choice design, there are no computationally feasible ways to verify that the resulting design is indeed optimal or efficient. In this article, an approach of evaluating the performance of the CEA for Bayesian optimal designs is proposed. This approach gives a lower bound of the efficiency of the resulting design under the continuous/approximate optimal design framework where well-established mathematical tools and theories can be modified and utilized. Empirical studies show that the CEA is highly efficient for deriving homogeneous optimal designs.