Daniels Michael J, Chatterjee Arkendu S, Wang Chenguang
Department of Statistics, University of Florida, Gainesville, FL 32611, USA.
Biometrics. 2012 Dec;68(4):1055-63. doi: 10.1111/j.1541-0420.2012.01766.x. Epub 2012 May 2.
We explore the use of a posterior predictive loss criterion for model selection for incomplete longitudinal data. We begin by identifying a property that most model selection criteria for incomplete data should consider. We then show that a straightforward extension of the Gelfand and Ghosh (1998, Biometrika, 85, 1-11) criterion to incomplete data has two problems. First, it introduces an extra term (in addition to the goodness of fit and penalty terms) that compromises the criterion. Second, it does not satisfy the aforementioned property. We propose an alternative and explore its properties via simulations and on a real dataset and compare it to the deviance information criterion (DIC). In general, the DIC outperforms the posterior predictive criterion, but the latter criterion appears to work well overall and is very easy to compute unlike the DIC in certain classes of models for missing data.
我们探讨将后验预测损失准则用于不完全纵向数据的模型选择。我们首先确定一个大多数不完全数据的模型选择标准应考虑的属性。然后我们表明，将Gelfand和Ghosh（1998年，《生物统计学》，85卷，1 - 11页）的准则直接扩展到不完全数据存在两个问题。首先，它引入了一个额外的项（除了拟合优度和惩罚项之外），这损害了该准则。其次，它不满足上述属性。我们提出了一种替代方法，并通过模拟和一个真实数据集探索其属性，还将其与偏差信息准则（DIC）进行比较。一般来说，DIC优于后验预测准则，但后验预测准则总体上似乎效果良好，并且与某些缺失数据模型类中的DIC不同，它非常易于计算。
