Identifiability and convergence behavior for Markov chain Monte Carlo using multivariate probit models.

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

Abstract

Multivariate probit models have been popularly utilized to analysis multivariate ordinal data. However, the identifiable multivariate probit models entail the covariance matrix for the underlying multivariate normal variables to be a correlation matrix, which brings a rigorous task to conduct efficient statistical analysis. Parameter expansion to make the identifiable model to be non-identifiable has been inevitably explored. However, the effect of the expanded parameters on the convergence of Markov chain Monte Carlo (MCMC) is seldomly investigated; in addition, the comparison of MCMC developed based on the identifiable model and that based on the non-identifiable model is hardly ever explored, especially for data with large sample sizes. In this paper, we conduct a thorough investigation to illustrate the effect of the expanded parameters on the convergence of MCMC and compare the behavior of MCMC between the identifiable and non-identifiable models. Our investigation provides a practical guide regarding the construction of non-identifiable models and development of corresponding MCMC sampling methods. We conduct our investigation using simulation studies and present an application using data from the Russia Longitudinal Monitoring Survey-Higher School of Economics (RLMS-HSE) study.

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马尔可夫链蒙特卡罗多变量概率模型的可辨识性和收敛性。
多元概率模型已被广泛用于分析多元有序数据。然而,可识别的多变量probit模型需要多变量正态变量的协方差矩阵为相关矩阵,这给进行高效的统计分析带来了艰巨的任务。将可识别模型扩展为不可识别模型是不可避免的探索。然而,展开参数对马尔可夫链蒙特卡罗(MCMC)收敛性的影响研究较少;此外,基于可识别模型的MCMC和基于不可识别模型的MCMC的比较很少被探索,特别是对于大样本量的数据。本文深入研究了扩展参数对MCMC收敛的影响,并比较了可识别模型和不可识别模型的MCMC行为。我们的研究为非识别模型的构建和相应MCMC采样方法的发展提供了实用指导。我们使用模拟研究进行调查,并使用俄罗斯纵向监测调查-高等经济学院(RLMS-HSE)研究的数据提出了一个应用程序。
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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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