Yang Mingan
Department of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859, USA.
Biom J. 2013 Mar;55(2):217-30. doi: 10.1002/bimj.201100149. Epub 2013 Jan 16.
In a linear mixed effects model, it is common practice to assume that the random effects follow a parametric distribution such as a normal distribution with mean zero. However, in the case of variable selection, substantial violation of the normality assumption can potentially impact the subset selection and result in poor interpretation and even incorrect results. In nonparametric random effects models, the random effects generally have a nonzero mean, which causes an identifiability problem for the fixed effects that are paired with the random effects. In this article, we focus on a Bayesian method for variable selection. We characterize the subject-specific random effects nonparametrically with a Dirichlet process and resolve the bias simultaneously. In particular, we propose flexible modeling of the conditional distribution of the random effects with changes across the predictor space. The approach is implemented using a stochastic search Gibbs sampler to identify subsets of fixed effects and random effects to be included in the model. Simulations are provided to evaluate and compare the performance of our approach to the existing ones. We then apply the new approach to a real data example, cross-country and interlaboratory rodent uterotrophic bioassay.
在线性混合效应模型中，通常的做法是假定随机效应服从参数分布，比如均值为零的正态分布。然而，在变量选择的情况下，严重违反正态性假设可能会对子集选择产生潜在影响，并导致解释不佳甚至结果错误。在非参数随机效应模型中，随机效应通常具有非零均值，这会给与随机效应配对的固定效应带来可识别性问题。在本文中，我们专注于一种用于变量选择的贝叶斯方法。我们用狄利克雷过程对特定个体的随机效应进行非参数刻画，并同时解决偏差问题。特别地，我们针对随机效应的条件分布提出了灵活建模，使其随预测变量空间发生变化。该方法通过随机搜索吉布斯采样器来实现，以识别模型中要包含的固定效应和随机效应的子集。我们提供了模拟来评估和比较我们的方法与现有方法的性能。然后，我们将新方法应用于一个实际数据示例，即跨国和跨实验室的啮齿动物子宫营养生物测定。
