Construction of symmetric paired choice experiments: minimising runs and maximising efficiency

Discrete choice experiments (DCEs) are popular in various fields such as health resources, marketing, transport, economics, and many others for identifying the factors that influence an individual’s choice behaviour. Selecting the DCE design is crucial in determining the observable effects. In this paper, the optimal form of the information matrix is introduced for attributes at two levels, main effect models, and equal choice probabilities for paired choice experiments. Additionally, the construction of D-optimal designs is modified to obtain DCEs when the number of attributes equals the number of runs, including designs with choice sets of sizes that are not necessarily multiples of 4, i.e. N ≢ 0mod4. The designs suggested in this paper have the same or higher D-efficiencies than existing efficient designs for the same number of choice sets. Moreover, the proposed design techniques can be extended to be applied to situations where the attributes of DCEs have a higher number of levels (ℓ > 2), resulting in designs with the same improved D-efficiencies and sufficiently small sample sizes. The designs proposed in this paper offer a notable advantage by allowing a reduction of 33% in the number of choice pairs with only a marginal loss of 11% in D-efficiency when compared to an optimal design. In comparison, the design suggested by other researchers incurs a higher loss in D-efficiency.