The Annals of Statistics

Fence methods for mixed model selection

Jiming Jiang, J. Sunil Rao, Zhonghua Gu, and Thuan Nguyen

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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.

Article information

Ann. Statist., Volume 36, Number 4 (2008), 1669-1692.

First available in Project Euclid: 16 July 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F07: Ranking and selection 62F35: Robustness and adaptive procedures
Secondary: 62F40: Bootstrap, jackknife and other resampling methods

Adaptive fence consistency F-B fence finite sample performance GLMM linear mixed model model selection


Jiang, Jiming; Rao, J. Sunil; Gu, Zhonghua; Nguyen, Thuan. Fence methods for mixed model selection. Ann. Statist. 36 (2008), no. 4, 1669--1692. doi:10.1214/07-AOS517.

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