Bayesian D-Optimal Choice Designs for Mixtures

Consumer products and services can often be described as mixtures of ingredients. Examples are the mixture of ingredients in a cocktail and the mixture of different components of waiting time (e.g., in-vehicle and out-of-vehicle travel time) in a transportation setting. Choice experiments may help to determine how the respondents' choice of a product or service is affected by the combination of ingredients. In such studies, individuals are confronted with sets of hypothetical products or services and they are asked to choose the most preferred product or service from each set. However, there are no studies on the optimal design of choice experiments involving mixtures. We propose a method for generating an optimal design for such choice experiments. To this end, we first introduce mixture models in the choice context and next present an algorithm to construct optimal experimental designs, assuming the multinomial logit model is used to analyze the choice data. To overcome the problem that the optimal designs depend on the unknown parameter values, we adopt a Bayesian D-optimal design approach. We also consider locally D-optimal designs and compare the performance of the resulting designs to those produced by a utility-neutral (UN) approach in which designs are based on the assumption that individuals are indifferent between all choice alternatives. We demonstrate that our designs are quite different and in general perform better than the UN designs.