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首页> 外文期刊>Transportation Research Part B: Methodological >Bayesian estimation of mixed multinomial logit models: Advances and simulation-based evaluations
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Bayesian estimation of mixed multinomial logit models: Advances and simulation-based evaluations

机译：混合多项式logit模型的贝叶斯估计：进展和基于仿真的评估

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摘要

Variational Bayes (VB) methods have emerged as a fast and computationally-efficient alternative to Markov chain Monte Carlo (MCMC) methods for scalable Bayesian estimation of mixed multinomial logit (MMNL) models. It has been established that VB is substantially faster than MCMC at practically no compromises in predictive accuracy. In this paper, we address two critical gaps concerning the usage and understanding of VB for MMNL. First, extant VB methods are limited to utility specifications involving only individual-specific taste parameters. Second, the finite-sample properties of VB estimators and the relative performance of VB, MCMC and maximum simulated likelihood estimation (MSLE) are not known. To address the former, this study extends several VB methods for MMNL to admit utility specifications including both fixed and random utility parameters. To address the latter, we conduct an extensive simulation-based evaluation to benchmark the extended VB methods against MCMC and MSLE in terms of estimation times, parameter recovery and predictive accuracy. The results suggest that all VB variants with the exception of the ones relying on an alternative variational lower bound constructed with the help of the modified Jensen's inequality perform as well as MCMC and MSLE at prediction and parameter recovery. In particular, VB with nonconjugate variational message passing and the delta-method (VB-NCVMP-Delta) is up to 16 times faster than MCMC and MSLE. Thus, VB-NCVMP-Delta can be an attractive alternative to MCMC and MSLE for fast, scalable and accurate estimation of MMNL models. (C) 2019 Elsevier Ltd. All rights reserved.
机译：对于混合多项式logit（MMNL）模型的可伸缩贝叶斯估计，变分贝叶斯（VB）方法已经成为马尔可夫链蒙特卡洛（MCMC）方法的一种快速且计算效率高的替代方法。已经确定的是，VB实际上比MCMC快得多，而实际上在预测精度上没有任何妥协。在本文中，我们解决了有关MMNL的VB使用和理解的两个关键空白。首先，现有的VB方法仅限于仅涉及个别特定口味参数的实用程序规范。其次，尚不了解VB估计器的有限样本属性以及VB，MCMC和最大模拟似然估计（MSLE）的相对性能。为了解决前者，本研究扩展了MMNL的几种VB方法，以接受实用程序规范，包括固定和随机实用程序参数。为了解决后者，我们进行了广泛的基于仿真的评估，以在估计时间，参数恢复和预测准确性方面针对MCMC和MSLE对扩展的VB方法进行基准测试。结果表明，除依赖于借助改进的詹森不等式构建的替代变分下界的VB变体以外，其他所有VB变体在预测和参数恢复方面的性能均与MCMC和MSLE相同。特别是，具有非共轭可变消息传递的VB和增量方法（VB-NCVMP-Delta）的速度比MCMC和MSLE快16倍。因此，对于MMNL模型的快速，可扩展和准确的估算，VB-NCVMP-Delta可能是MCMC和MSLE的有吸引力的替代方案。 （C）2019 Elsevier Ltd.保留所有权利。

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