Fence methods for mixed model selection

By Jiming Jiang, J. Sunil Rao, Zhonghua Gu, Thuan Nguyen. 2008

102 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability

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Citations in the corpus

Forward stability and model path selection (2021, neutral): “Jiang et al. (2008) proposed a “fence” method to weed out poor-performing models from M in hopes of obtaining some reduced set M ∗ that contains the optimal model with high probability.”
Model Selection in Linear Mixed Models (2013, methodology): “, Dimova, Markatou and Talal, 2011; Kubokawa (2011)). One exception is Ahn, Zhang and Lu (2012) who propose a model selection method based on moment estimation which does not require any distributional assumptions.”
New important developments in small area estimation (2013, methodology): “Jiang et al. (2008) propose a class of strategies for mixed model selection called fence methods, which apply to LMM and GLMM.”
Model Selection by Testing for the Presence of Small-Area Effects, and Application to Area-Level Data (2011, methodology): “In this context, consistent model selection procedures are developed in Jiang and Rao (2003), Jiang et al. (2008), and Jiang, Nguyen, and Rao (2010).”
A note on BIC in mixed-effects models (2014, background): “[10] pointed out the difficulties encountered with these criteria in non conventional situations including mixed models and introduced new strategies called fence methods.”
Cross-Validation With Confidence (2017, methodology): “This is comparable to other model selection methods based on bootstrap and resampling methods such as the “fence” method [19].”