Parameter-expanded data augmentation for analyzing multinomial probit models.

IF 0.8 4区 数学 Q4 STATISTICS & PROBABILITY
Xiao Zhang
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引用次数: 0

Abstract

The multinomial probit model has been a prominent tool to analyze nominal categorical data, but the computational complexity of maximum likelihood functions presents challenges in the usage of this model. Furthermore, the model identification is extremely tenuous and usually necessitates the covariance matrix of the latent multivariate normal variables to be a restricted covariance matrix, which brings a rigorous task for both likelihood-based estimation and Markov chain Monte Carlo (MCMC) sampling. We tackle this issue by constructing a non-identifiable model and developing parameter-expanded data augmentation. Our proposed methods circumvent sampling a restricted covariance matrix commonly implemented by a painstaking Metropolis-Hastings (MH) algorithm and enable to sample a covariance matrix without restriction through a Gibbs sampler. Therefore, our proposed methods advance the convergence and mixing of the MCMC components considerably. We investigate our proposed methods along with the method based on the identifiable model through simulation studies and further illustrate their performance by an application to consumer choice on liquid laundry detergents data.

分析多项概率模型的参数扩展数据扩充。
多项概率模型已成为分析名义分类数据的重要工具,但极大似然函数的计算复杂性给该模型的使用带来了挑战。此外,模型辨识非常脆弱,通常需要多元潜正态变量的协方差矩阵是一个受限协方差矩阵,这给基于似然估计和马尔可夫链蒙特卡罗(MCMC)抽样带来了严格的任务。我们通过构建一个不可识别的模型和开发参数扩展数据增强来解决这个问题。我们提出的方法绕过了通常由辛苦的Metropolis-Hastings (MH)算法实现的限制性协方差矩阵的采样,并且能够通过Gibbs采样器对协方差矩阵进行无限制采样。因此,我们提出的方法大大促进了MCMC组件的收敛和混合。我们通过仿真研究对我们提出的方法以及基于可识别模型的方法进行了研究,并通过消费者对洗衣液的选择数据的应用进一步说明了它们的性能。
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来源期刊
CiteScore
2.00
自引率
12.50%
发文量
320
审稿时长
7.5 months
期刊介绍: The Theory and Methods series intends to publish papers that make theoretical and methodological advances in Probability and Statistics. New applications of statistical and probabilistic methods will also be considered for publication. In addition, special issues dedicated to a specific topic of current interest will also be published in this series periodically, providing an exhaustive and up-to-date review of that topic to the readership.
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