A Comparison of Different Bayesian Design Criteria to Compute Efficient Conjoint Choice Experiments

Abstract

Bayesian design theory applied to nonlinear models is a promising route to cope with the problem of design dependence on the unknown parameters. The traditional Bayesian design criterion which is often used in the literature is derived from the second derivatives of the loglikelihood function. However, other design criteria are possible. Examples are design criteria based on the second derivative of the log posterior density, the expected posterior covariance matrix, or on the amount of information provided by the experiment. Not much is known in general about how well these criteria perform in constructing efficient designs and which criterion yields robust designs that are efficient for various parameter values. In this study, we apply these Bayesian design criteria to conjoint choice experimental designs and investigate how robust the resulting Bayesian optimal designs are with respect to other design criteria for which they were not optimized. We also examine the sensitivity of each design criterion to the prior distribution. Finally, we try to find out which design criterion is most appealing in a non-Bayesian framework where it is accepted that prior information must be used for design but should not be used in the analysis, and which one is most appealing in a Bayesian framework when the prior distribution is taken into account both for design and for analysis.