通过偏自相关和边际方差对纵向数据中的依赖性进行贝叶斯建模。
Bayesian modeling of the dependence in longitudinal data via partial autocorrelations and marginal variances.
作者信息
Wang Y, Daniels M J
机构信息
Department of Biostatistics University of Florida Dauer Hall Gainesville, Florida 32611
出版信息
J Multivar Anal. 2013 Apr 1;116:130-140. doi: 10.1016/j.jmva.2012.11.010.
Many parameters and positive-definiteness are two major obstacles in estimating and modelling a correlation matrix for longitudinal data. In addition, when longitudinal data is incomplete, incorrectly modelling the correlation matrix often results in bias in estimating mean regression parameters. In this paper, we introduce a flexible and parsimonious class of regression models for a covariance matrix parameterized using marginal variances and partial autocorrelations. The partial autocorrelations can freely vary in the interval (-1, 1) while maintaining positive definiteness of the correlation matrix so the regression parameters in these models will have no constraints. We propose a class of priors for the regression coefficients and examine the importance of correctly modeling the correlation structure on estimation of longitudinal (mean) trajectories and the performance of the DIC in choosing the correct correlation model via simulations. The regression approach is illustrated on data from a longitudinal clinical trial.
许多参数和正定是纵向数据相关矩阵估计和建模中的两个主要障碍。此外，当纵向数据不完整时，对相关矩阵进行错误建模通常会导致估计均值回归参数时出现偏差。在本文中，我们引入了一类灵活且简约的回归模型，用于协方差矩阵，该矩阵使用边际方差和偏自相关进行参数化。偏自相关可以在区间（-1, 1）内自由变化，同时保持相关矩阵的正定，因此这些模型中的回归参数将没有约束。我们为回归系数提出了一类先验，并通过模拟研究了正确建模相关结构对纵向（均值）轨迹估计的重要性以及DIC在选择正确相关模型方面的性能。通过一项纵向临床试验的数据说明了回归方法。
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