Fence methods for mixed model selection

TL;DR

This paper introduces fence methods for mixed model selection, providing a flexible, consistent approach to identify optimal models in complex settings where traditional criteria struggle.

Contribution

It proposes a new class of fence procedures for mixed models, including stepwise and adaptive variations, with theoretical consistency guarantees.

Findings

Fence methods effectively select models in simulations.

The methods perform well on real data examples.

Consistency of the procedures is theoretically established.

Abstract

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.