Bayesian optimal designs for discrete choice experiments with partial profiles

In a discrete choice experiment, each respondent chooses the best product or service sequentially from many groups or choice sets of alternative goods. The alternatives are described by levels of a set of predefined attributes and are also referred to as profiles. Respondents often find it difficult to trade of prospective goods when every attribute of the offering changes in each comparison. Especially in studies involving many attributes, respondents get overloaded by the complexity of the choice task. To overcome respondent fatigue, it is better to simplify the choice tasks by holding the levels of some of the attributes constant in every choice set. The resulting designs are called partial profile designs. In this paper, we construct D-optimal partial profile designs for estimating main-effects models. We use a Bayesian design algorithm that integrates the D-optimality criterion over a prior distribution of likely parameter values. To determine the constant attributes in each choice set, we generalize the approach that makes use of balanced incomplete block designs. Our algorithm is very fexible because it produces partial profile designs of any choice set size and allows for attributes with any number of levels and any number of constant attributes. We provide an illustration in which we make recommendations that balance the loss of statistical information and the burden imposed on the respondents.