An R2 statistic for covariance model selection in the linear mixed model

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 $ R^2 $ R2 have been proposed for the linear mixed model, but several limitations prevail. Presently, there is no method to compute $ R^2 $ R2 for the linear mixed model that accommodates an interpretation based on variance partitioning, a method to quantify uncertainty and produce confidence limits for the $ R^2 $ R2 statistic, and a capacity to use the $ R^2 $ R2 statistic to conduct covariance model selection in a manner similar to information criteria. In this article, we introduce such an $ R^2 $ R2 statistic. The proposed $ R^2 $ R2 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 $ R^2 $ R2 and its capacity to be applied to covariance model selection.