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Parameter-expanded data augmentation for analyzing correlated binary data using multivariate probit models.
Statistics in Medicine ( IF 1.8 ) Pub Date : 2020-07-24 , DOI: 10.1002/sim.8685
Xiao Zhang 1
Affiliation  

Data augmentation has been commonly utilized to analyze correlated binary data using multivariate probit models in Bayesian analysis. However, the identification issue in the multivariate probit models necessitates a rigorous Metropolis‐Hastings algorithm for sampling a correlation matrix, which may cause slow convergence and inefficiency of Markov chains. It is well‐known that the parameter‐expanded data augmentation, by introducing a working/artificial parameter or parameter vector, makes an identifiable model be non‐identifiable and improves the mixing and convergence of data augmentation components. Therefore, we motivate to develop efficient parameter‐expanded data augmentations to analyze correlated binary data using multivariate probit models. We investigate both the identifiable and non‐identifiable multivariate probit models and develop the corresponding parameter‐expanded data augmentation algorithms. We point out that the approaches, based on one non‐identifiable model, circumvent a Metropolis‐Hastings algorithm for sampling a correlation matrix and improve the convergence and mixing of correlation parameters; the identifiable model may produce the estimated regression parameters with smaller standard errors than the non‐identifiable model does. We illustrate our proposed approaches using simulation studies and through the application to a longitudinal dataset from the Six Cities study.

中文翻译:

使用多变量概率模型分析相关二进制数据的参数扩展数据扩充。

在贝叶斯分析中,通常使用数据增强来使用多元概率模型分析相关的二进制数据。但是,多元概率模型中的识别问题需要采用严格的Metropolis-Hastings算法对相关矩阵进行采样,这可能会导致Markov链收敛缓慢且效率低下。众所周知,通过引入工作/人工参数或参数向量,参数扩展的数据扩充使可识别的模型变得不可识别,并改善了数据扩充组件的混合和融合。因此,我们激励开发有效的参数扩展数据扩充,以使用多元概率模型分析相关的二进制数据。我们研究了可识别和不可识别的多元概率模型,并开发了相应的参数扩展数据扩充算法。我们指出,这些方法基于一种不可识别的模型,绕过了Metropolis-Hastings算法来对相关矩阵进行采样,并改善了相关参数的收敛性和混合性。可识别模型所产生的估计回归参数具有比不可识别模型小的标准误差。我们使用仿真研究以及通过应用到六座城市的纵向数据集中来说明我们提出的方法。规避Metropolis-Hastings算法对相关矩阵进行采样,并改善相关参数的收敛和混合;可识别模型所产生的估计回归参数具有比不可识别模型小的标准误差。我们使用仿真研究以及通过应用到六座城市的纵向数据集中来说明我们提出的方法。规避Metropolis-Hastings算法对相关矩阵进行采样,并改善相关参数的收敛和混合;可识别模型所产生的估计回归参数具有比不可识别模型小的标准误差。我们通过模拟研究以及通过对六座城市研究的纵向数据集的应用,说明了我们提出的方法。
更新日期:2020-10-02
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