Optimal experimental designs for conjoint analysis: Estimation of utility functions

In conjoint analysis consumers utility functions over multiattributed stimuli are estimated using experimental data. The quality of these estimations heavily depends on the alternatives presented in the experiment. An efficient selection of the experiment design matrix allows more information to be elicited about consumer preferences from a small number of questions, thus reducing experimental cost and respondent’s fatigue. Kiefer’s methodology considers approximate optimal design selecting the same combination of stimuli more than once. In the context of conjoint analysis, replications do not make sense for individual respondents. We present a general approach to compute optimal designs for conjoint experiments in a variety of scenarios and methodologies: continuous, discrete and mixed attributes types, customer panels with random effects, and quantile regression models. We do not compute good designs, but the best ones according to the size (determinant or trace) of the information matrix of the associated estimators without repeating profiles as in Kiefer’s methodology. We use efficient optimization algorithms to achieve our goal.