Bayesian analysis of covariance matrices and dynamic models for longitudinal data
Bayesian analysis of covariance matrices and dynamic models for longitudinal data
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DOI：
10.1093/biomet/89.3.553
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发表时间：
2002-09-01
期刊：
影响因子：
2.7
通讯作者：
Pourahmadi, M
中科院分区：
文献类型：
--
作者：
Daniels, MJ;Pourahmadi, M
在纵向数据分析中，在注意其正定性的同时，对受试者内协方差结构进行简约建模是非常重要的。使用Cholesky分解和随后的无约束和统计上有意义的reparameterisation，我们提供了一个方便和直观的框架，开发条件共轭先验分布的协方差矩阵，并显示其与广义逆Wishart先验的连接。我们的先验提供了许多优点，关于启发，正定性，计算使用吉布斯抽样，收缩协方差对一个特定的结构具有相当大的灵活性，协方差建模使用协变量。贝叶斯估计方法的开发和使用两个模拟研究的结果进行了比较。这些模拟建议更简单，更合适的纵向数据的协方差结构的先验。
Parsimonious modelling of the within-subject covariance structure while heeding its positive-definiteness is of great importance in the analysis of longitudinal data. Using the Cholesky decomposition and the ensuing unconstrained and statistically meaningful reparameterisation, we provide a convenient and intuitive framework for developing conditionally conjugate prior distributions for covariance matrices and show their connections with generalised inverse Wishart priors. Our priors offer many advantages with regard to elicitation, positive definiteness, computations using Gibbs sampling, shrinking covariances toward a particular structure with considerable flexibility, and modelling covariances using covariates. Bayesian estimation methods are developed and the results are compared using two simulation studies. These simulations suggest simpler and more suitable priors for the covariance structure of longitudinal data.