Gaskins Jeremy T, Daniels Michael J
Department of Statistics, University of Florida, Gainesville, Florida 32611.
Biometrika. 2013;100(1). doi: 10.1093/biomet/ass060.
In the modeling of longitudinal data from several groups, appropriate handling of the dependence structure is of central importance. Standard methods include specifying a single covariance matrix for all groups or independently estimating the covariance matrix for each group without regard to the others, but when these model assumptions are incorrect, these techniques can lead to biased mean effects or loss of efficiency, respectively. Thus, it is desirable to develop methods to simultaneously estimate the covariance matrix for each group that will borrow strength across groups in a way that is ultimately informed by the data. In addition, for several groups with covariance matrices of even medium dimension, it is difficult to manually select a single best parametric model among the huge number of possibilities given by incorporating structural zeros and/or commonality of individual parameters across groups. In this paper we develop a family of nonparametric priors using the matrix stick-breaking process of Dunson et al. (2008) that seeks to accomplish this task by parameterizing the covariance matrices in terms of the parameters of their modified Cholesky decomposition (Pourahmadi, 1999). We establish some theoretic properties of these priors, examine their effectiveness via a simulation study, and illustrate the priors using data from a longitudinal clinical trial.
在对多组纵向数据进行建模时，对依赖结构进行适当处理至关重要。标准方法包括为所有组指定单个协方差矩阵，或独立估计每个组的协方差矩阵而不考虑其他组，但当这些模型假设不正确时，这些技术可能分别导致均值效应有偏差或效率损失。因此，需要开发方法来同时估计每个组的协方差矩阵，以便以最终由数据决定的方式在组间借用强度。此外，对于协方差矩阵维度适中的多个组，在通过纳入结构零和/或跨组单个参数的共性所给出的大量可能性中手动选择单个最佳参数模型是困难的。在本文中，我们使用Dunson等人（2008年）的矩阵折断过程开发了一族非参数先验，该过程旨在通过根据其修正的Cholesky分解（Pourahmadi，1999年）的参数对协方差矩阵进行参数化来完成此任务。我们建立了这些先验的一些理论性质，通过模拟研究检验它们的有效性，并使用来自纵向临床试验的数据说明这些先验。
