  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.
