Accounting for model uncertainty in individualized designs for discrete choice experiments

We develop a method for finding optimal designs in Discrete Choice Experiments (DCEs). More specifically, we deal with individualized designs, which are sequentially generated for each person undertaking a survey, using - at each stage - responses from previous choice sets in order to select the next best set. Currently the optimal design for a DCE is predicated on a specific mixed logit model which represents the probability of choosing a specific alternative in a choice set through a linear predictor combining several attributes or factors deemed to be relevant in each choice. Using a unique model represents a major limitation which we overcome by allowing for a collection of different models characterized by distinct linear predictors. Our approach is fully Bayesian and incorporates a prior distribution on the model space, as well as a prior on the parameter space specific to each respondent. To perform our optimal design strategy for DCEs, we specify two distinct utility functions, one being targeted to model discrimination, while the other aims at the dual purpose of model discrimination and parameter estimation. We implement our methodology using a sequential Monte Carlo algorithm suitably tailored to account for model uncertainty and individual-specific parameters. To evaluate our methodology, several simulation settings are considered in detail. Comparisons with alternative methods are also investigated.