论文标题
多项式概率模型中可扩展的贝叶斯估计
Scalable Bayesian estimation in the multinomial probit model
论文作者
论文摘要
多项式概率模型是分析选择行为的流行工具，因为它允许选择替代方案之间的相关性。由于当前的模型规格采用了选择替代方案的潜在公用事业的完整协方差矩阵，因此它们不可扩展到大量选择替代方案。本文提出了协方差矩阵上的一个因子结构，这使该模型可扩展到大型选择集。估计该结构的主要挑战是模型参数需要识别限制。我们通过在协方差矩阵上的痕量限制来识别参数，该参数是通过对因子结构的重新分析而施加的。我们在模型参数上指定可解释的先验分布，并为参数估计开发MCMC采样器。相对于现有的多项式概率规范，所提出的方法可显着提高大型选择集的性能。购买数据的应用表明，在消费者选择分析中包括大量选择替代方案的经济重要性。
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.
