A comparison of different Bayesian design criteria for setting up stated preference studies

The design of stated preference studies has received much attention in the recent transportation literature. The research has led to a paradigm shift in that optimal experimental design is now considered the state-of-the-art design approach for these kinds of studies. The optimal experimental design approach for stated preference studies, as presented in the literature, is Bayesian in nature and builds on the Fisher information matrix. The Bayesian approach is necessary for coping with the problem that the optimal design depends on the unknown parameters in the stated choice model. However, the reliance of the approach on maximum likelihood estimation of the logit models of interest and on the corresponding Fisher information matrix (and its inverse) is a weakness. This is because maximum likelihood is known to produce biased estimates for finite sample sizes and the Fisher information matrix, used to evaluate the quality of stated preference designs and to perform hypothesis tests, is only asymptotically valid. In this article, we study various alternatives to the Fisher information matrix as a basis for constructing Bayesian optimal designs for stated preference studies. The alternatives we consider to quantify the information content of a stated preference study are known to have better finite sample properties than the Fisher information matrix, because they are based on Bayesian estimation procedures that are considered more appropriate than maximum likelihood procedures when the sample size is small. We compare designs based on the Fisher information matrix with designs based on the generalized Fisher information matrix, the expected posterior covariance matrix, and the expected gain in Shannon information. We perform our comparison in a scenario where a Bayesian analysis is performed as well as in a scenario in which maximum likelihood estimation is used. Our simulation results favor Bayesian design criteria based on the generalized Fisher information matrix and on the expected posterior covariance matrix. For computational reasons, we recommend using the generalized Fisher information matrix as a basis for determining efficient designs for stated preference studies.

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