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

机译：设置陈述性偏好研究的不同贝叶斯设计标准的比较

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摘要

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.
机译：陈述偏好研究的设计在最近的运输文献中受到了很多关注。这项研究导致了范式的转变，因为现在已经将最佳实验设计视为这类研究的最新设计方法。如文献所述，用于陈述偏好研究的最佳实验设计方法本质上是贝叶斯方法，并建立在Fisher信息矩阵的基础上。贝叶斯方法对于解决最优设计取决于所述选择模型中的未知参数的问题是必要的。但是，该方法依赖于感兴趣的Logit模型的最大似然估计以及相应的Fisher信息矩阵（及其逆矩阵）是一个弱点。这是因为已知最大似然会产生有限样本量的有偏估计，而用于评估陈述的偏好设计的质量并执行假设检验的Fisher信息矩阵只是渐近有效的。在本文中，我们研究了Fisher信息矩阵的各种替代方法，以此作为构建针对陈述偏好研究的贝叶斯最优设计的基础。我们认为用来量化陈述式偏好研究的信息内容的替代方法具有比Fisher信息矩阵更好的有限样本属性，因为它们基于贝叶斯估计程序，当样本量为10时，被认为比最大似然程序更合适。小。我们将基于Fisher信息矩阵的设计与基于广义Fisher信息矩阵，预期后验协方差矩阵和Shannon信息的预期增益的设计进行比较。我们在执行贝叶斯分析的场景以及使用最大似然估计的场景中进行比较。我们的仿真结果支持基于广义Fisher信息矩阵和预期后验协方差矩阵的贝叶斯设计准则。出于计算原因，我们建议使用广义Fisher信息矩阵作为确定陈述性偏好研究的有效设计的基础。

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