Many model search strategies involve trading off model fit with modelcomplexity in a penalized goodness of fit measure. Asymptotic properties forthese types of procedures in settings like linear regression and ARMA timeseries have been studied, but these do not naturally extend to nonstandardsituations such as mixed effects models, where simple definition of the samplesize is not meaningful. This paper introduces a new class of strategies, knownas fence methods, for mixed model selection, which includes linear andgeneralized linear mixed models. The idea involves a procedure to isolate asubgroup of what are known as correct models (of which the optimal model is amember). This is accomplished by constructing a statistical fence, or barrier,to carefully eliminate incorrect models. Once the fence is constructed, theoptimal model is selected from among those within the fence according to acriterion which can be made flexible. In addition, we propose two variations ofthe fence. The first is a stepwise procedure to handle situations of manypredictors; the second is an adaptive approach for choosing a tuning constant.We give sufficient conditions for consistency of fence and its variations, adesirable property for a good model selection procedure. The methods areillustrated through simulation studies and real data analysis.
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