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

Byron C. Jaeger, Lloyd J. Edwards and Matthew J. Gurka

Journal of Applied Statistics, 2019, vol. 46, issue 1, 164-184

Abstract: 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.

Date: 2019
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DOI: 10.1080/02664763.2018.1466869

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