Bayesian nonparametric estimation and consistency of mixed multinomial logit choice models
Bayesian nonparametric estimation and consistency of mixed multinomial logit choice models
复制标题
混合多项Logit选择模型的贝叶斯非参数估计和一致性
作者：
P. Blasi;Lancelot F. James;J. Lau
基于混合多项Logit(MMNL)模型，提出了离散选择模型的非参数估计。本文证明了MMNL模型包含了在随机效用最大化假设下导出的所有离散选择模型，但需要识别未知分布G。注意到MMNL的混合模型描述，我们使用贝叶斯非参数方法，利用未知混合分布G的非参数先验来估计未知选择概率。通过在简单充分的条件下建立G上一般非参数先验的强相合性，为所提方法的使用提供了理论支持。一致性是根据选择概率空间上的L1型距离定义的，并通过将最近基于先验概率平方根和的强一致性的方法扩展到回归模型框架来实现。转到估计，讨论了非面板数据模型和面板数据模型的略有不同的技术。对于实际实施，我们描述了有效且相对容易使用的块Gibbs抽样过程。文中还进行了仿真研究，以说明所提出的方法以及它们相对于参数高斯MMNL模型所实现的灵活性。
This paper develops nonparametric estimation for discrete choice models based on the Mixed Multinomial Logit (MMNL) model. It has been shown that MMNL models encompass all discrete choice models derived under the assumption of random utility maximization, subject to the identification of an unknown distribution G. Noting the mixture model description of the MMNL, we employ a Bayesian nonparametric approach, using nonparametric priors on the unknown mixing distribution G, to estimate the unknown choice probabilities. Theoretical support for the use of the proposed methodology is provided by establishing strong consistency of a general nonparametric prior on G under simple sufficient conditions. Consistency is defined according to a L1-type distance on the space of choice probabilities and is achieved by extending to a regression model framework a recent approach to strong consistency based on the summability of square roots of prior probabilities. Moving to estimation, slightly different techniques for non-panel and panel data models are discussed. For practical implementation, we describe efficient and relatively easy to use blocked Gibbs sampling procedures. A simulation study is also performed to illustrate the proposed methods and the exibility they achieve with respect to parametric Gaussian MMNL models.