Individually Adapted Sequential Bayesian Designs for Conjoint Choice Experiments

In this paper, we propose an efficient individually adapted sequential Bayesian approach for constructing conjoint choice experiments. It uses Bayesian updating, a Bayesian analysis and a Bayesian design criterion for generating choice-set-designs for each individual respondent based on previous answers of that particular respondent. The proposed design approach is compared with two non-adaptive design approaches (the average customization design proposed by Arora and Huber 2001 and the nearly orthogonal design constructed with Sawtooth software) under various degree of response error and respondent heterogeneity. The simulation study shows that the individually adapted sequential Bayesian approach leads to designs which are robust not only to respondent heterogeneity but also to response error. It turns out that the proposed method outperforms the benchmark methods in all scenarios that we have looked at. In particular, for conditions with high response error (the responses from a respondent can hardly provide proper information about the individual-level parameter and is therefore very challenging for individually adapted choice designs), our approach leads to substantially improvement not only in the precision of the parameter estimates but also in the predictive accuracy when the respondent heterogeneity is large. The new method therefore overcomes the limitation of the recently proposed adaptive polyhedral choice-based question design approach by Toubia et al. (2004), whose method performs well only when the response error is low. Furthermore, our study provides compelling evidence that adapting each respondent's choice sets based on the previous responses of that particular respondent in a Bayesian framework enables one to capture more information for the individual-level parameters and therefore also on the population-level parameters. It is shown that it is substantially better to employ the adaptive approach when the response heterogeneity is high