HIERARCHICAL SELECTION OF FIXED AND RANDOM EFFECTS IN GENERALIZED LINEAR MIXED MODELS
HIERARCHICAL SELECTION OF FIXED AND RANDOM EFFECTS IN GENERALIZED LINEAR MIXED MODELS
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DOI：
10.5705/ss.202015.0329
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发表时间：
2017-04-01
影响因子：
1.4
通讯作者：
Welsh, A. H.
中科院分区：
文献类型：
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作者：
Hui, Francis K. C.;Mueller, Samuel;Welsh, A. H.
在广义线性混合模型（glmm）的许多应用中，在进行变量选择时需要考虑效应的层次结构。这方面的一个主要例子是当将混合模型拟合到纵向数据时，协变量通常仅作为固定效应或复合（固定和随机）效应包括在内。在本文中，我们提出了第一种可以处理大量候选glmm的正则化方法，同时保留了这种层次结构：用于混合模型中联合选择的CREPE （Composite Random Effects PEnalty）。CREPE以分层方式诱导稀疏性，因为协变量的固定效应只有在相应的随机效应已经或已经缩小到零时才会缩小到零。在固定效应数量增长速度低于集群数量增长速度的情况下，我们证明了CREPE对于固定效应和随机效应都是选择一致的，并且达到了oracle属性。仿真结果表明，对于混合模型，CREPE优于现有的一些惩罚方法。
In many applications of generalized linear mixed models (GLMMs), there is a hierarchical structure in the effects that needs to be taken into account when performing variable selection. A prime example of this is when fitting mixed models to longitudinal data, where it is usual for covariates to be included as only fixed effects or as composite (fixed and random) effects. In this article, we propose the first regularization method that can deal with large numbers of candidate GLMMs while preserving this hierarchical structure: CREPE (Composite Random Effects PEnalty) for joint selection in mixed models. CREPE induces sparsity in a hierarchical manner, as the fixed effect for a covariate is shrunk to zero only if the corresponding random effect is or has already been shrunk to zero. In the setting where the number of fixed effects grow at a slower rate than the number of clusters, we show that CREPE is selection consistent for both fixed and random effects, and attains the oracle property. Simulations show that CREPE outperforms some currently available penalized methods for mixed models.