多项probit模型中的可伸缩贝叶斯估计
Scalable Bayesian estimation in the multinomial probit model
摘要：
多项概率模型是分析选择行为的流行工具，因为它允许选择方案之间的相关性。由于目前的模型规范采用了一个完整的协方差矩阵的潜在效用的选择方案，他们是不可扩展的大量的选择方案。本文提出了一种因子结构的协方差矩阵，这使得模型可扩展到大的选择集。估计这种结构的主要挑战是模型参数需要识别限制。我们通过对协方差矩阵的跟踪限制来识别参数，该限制是通过因子结构的重新参数化来施加的。我们指定可解释的先验分布的模型参数和开发MCMC采样器的参数估计。所提出的方法显着提高了性能，在大的选择集相对于现有的多项式probit规格。购买数据的应用表明，包括大量的选择替代品在消费者选择分析的经济重要性。
英文摘要：
The multinomial probit model is a popular tool for analyzing choice behaviour as it allows for correlation between choice alternatives. Because current model specifications employ a full covariance matrix of the latent utilities for the choice alternatives, they are not scalable to a large number of choice alternatives. This paper proposes a factor structure on the covariance matrix, which makes the model scalable to large choice sets. The main challenge in estimating this structure is that the model parameters require identifying restrictions. We identify the parameters by a trace-restriction on the covariance matrix, which is imposed through a reparametrization of the factor structure. We specify interpretable prior distributions on the model parameters and develop an MCMC sampler for parameter estimation. The proposed approach significantly improves performance in large choice sets relative to existing multinomial probit specifications. Applications to purchase data show the economic importance of including a large number of choice alternatives in consumer choice analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
