A-optimal and A-efficient designs for discrete choice experiments

Discrete choice experiments are widely used in fields such as marketing, planning, transportation, and medical care to obtain information on consumer preferences. In such experiments, choice sets consisting of two or more profiles are presented to subjects, where a profile consists of a set of attributes (as a list or picture) which describe the product or process. Subjects are asked to select their most preferred profile from each choice set, and the importance of the attributes can be deduced from the choices made.This paper investigates locally A-optimal designs for estimating main effects of the attributes, together with their interactions, under the multinomial logit model. Lower bounds are derived for the average variance of any set of orthonormal contrasts of interest. A new approach is proposed for generating locally A-optimal or A-efficient designs. It is shown through examples that the new construction method enables highly efficient designs to be constructed without a complete search.