An R~2 statistic for covariance model selection in the linear mixed model

摘要

The linear mixed model, sometimes referred to as the multi-level model, is one of the most widely used tools for analyses involving clustered data. Various definitions of have been proposed for the linear mixed model, but several limitations prevail. Presently, there is no method to compute for the linear mixed model that accommodates an interpretation based on variance partitioning, a method to quantify uncertainty and produce confidence limits for the statistic, and a capacity to use the statistic to conduct covariance model selection in a manner similar to information criteria. In this article, we introduce such an statistic. The proposed measures the proportion of generalized variance explained by fixed effects in the linear mixed model. Simulated and real longitudinal data are used to illustrate the statistical properties of the proposed and its capacity to be applied to covariance model selection.