Fence methods for mixed model selection
Fence methods for mixed model selection
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DOI：
10.1214/07-aos517
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发表时间：
2008-08-01
影响因子：
4.5
通讯作者：
Nguyen, Thuan
中科院分区：
文献类型：
--
作者：
Jiang, Jiming;Rao, J. Sunil;Nguyen, Thuan
许多模型搜索策略涉及在惩罚的拟合优度度量中权衡模型拟合与模型复杂性。已经研究了这些类型的程序在线性回归和阿尔马时间序列等设置中的渐近性质，但这些并不自然地扩展到非标准情况，如混合效应模型，其中简单定义样本量是没有意义的。本文介绍了一类新的策略，称为栅栏方法，混合模型选择，其中包括线性和广义线性混合模型。这个想法涉及到一个程序，以隔离一个所谓的正确模型（其中最佳模型是一个成员）的子组。这是通过构建一个统计围栏或障碍来实现的，以仔细消除不正确的模型。一旦构造了围栏，就根据可以变得灵活的标准从围栏内的那些模型中选择最优模型。此外，我们还提出了两种不同的围栏。第一个是一个逐步的过程来处理许多预测的情况下，第二个是一个自适应的方法来选择一个调谐常数。我们给出了栅栏及其变化的一致性的充分条件，这是一个良好的模型选择过程的理想属性。通过仿真研究和真实的数据分析说明了该方法。
Many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure. Asymptotic properties for these types of procedures in settings like linear regression and ARMA time series have been studied, but these do not naturally extend to nonstandard situations such as mixed effects models, where simple definition of the sample size is not meaningful. This paper introduces a new class of strategies, known as fence methods, for mixed model selection, which includes linear and generalized linear mixed models. The idea involves a procedure to isolate a subgroup of what are known as correct models (of which the optimal model is a member). This is accomplished by constructing a statistical fence, or barrier, to carefully eliminate incorrect models. Once the fence is constructed, the optimal model is selected from among those within the fence according to a criterion which can be made flexible. In addition, we propose two variations of the fence. The first is a stepwise procedure to handle situations of many predictors; the second is an adaptive approach for choosing a tuning constant. We give sufficient conditions for consistency of fence and its variations, a desirable property for a good model selection procedure. The methods are illustrated through simulation studies and real data analysis.