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Bayesian analysis of joint mean and covariance models for longitudinal data

机译：纵向数据联合均值和协方差模型的贝叶斯分析

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摘要

Efficient estimation of the regression coefficients in longitudinal data analysis requires a correct specification of the covariance structure. If misspecification occurs, it may lead to inefficient or biased estimators of parameters in the mean. One of the most commonly used methods for handling the covariance matrix is based on simultaneous modeling of the Cholesky decomposition. Therefore, in this paper, we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a fully Bayesian inference for joint mean and covariance models based on this decomposition. A computational efficient Markov chain Monte Carlo method which combines the Gibbs sampler and Metropolis-Hastings algorithm is implemented to simultaneously obtain the Bayesian estimates of unknown parameters, as well as their standard deviation estimates. Finally, several simulation studies and a real example are presented to illustrate the proposed methodology.
机译：在纵向数据分析中有效估计回归系数需要正确指定协方差结构。如果发生错误指定，则可能导致均值中的参数估算器效率低下或出现偏差。处理协方差矩阵的最常用方法之一是基于Cholesky分解的同时建模。因此，在本文中，我们通过对自身的改进的Cholesky分解对纵向数据分析中的协方差结构进行重新参数化。基于此改进的Cholesky分解，将受试者内部协方差矩阵分解为包含移动平均系数的单元下三角矩阵和涉及创新方差的对角矩阵，将其建模为协变量的线性函数。然后，我们基于此分解为联合均值和协方差模型提出了完全贝叶斯推断。实现了一种计算有效的马尔可夫链蒙特卡罗方法，该方法将Gibbs采样器和Metropolis-Hastings算法结合在一起，可以同时获取未知参数的贝叶斯估计及其标准偏差估计。最后，通过一些仿真研究和一个实际例子来说明所提出的方法。

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