An R2 Statistic for Covariance Model Selection in the Linear Mixed Model

• Activity Number: 163 - SPEED: Longitudinal/Correlated Data
• Type: Contributed
• Date/Time: Monday, July 30, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Byron Jaeger* and Lloyd Edwards and Matthew Gurka
• Companies: University of Alabama at Birmingham and University of Alabama at Birmingham and University of Florida
• Keywords: R-squared; linear mixed model; longitudinal data; covariance model selection; goodness-of-fit; random effects

Abstract

The linear mixed model (LMM), sometimes referred to as the multi-level model, stands as one of the most widely used tools for analyses involving clustered data. Various de?nitions of R-squared have been proposed for the LMM, but several limitations prevail. Presently there is no de?nition of R-squared in the LMM that accomodates (1) an interpretation based on variance partitioning, (2) a method to quantify uncertainty and produce con?dence limits, and (3) a capacity to conduct covariance model selection in a manner similar to information criteria. We introduce an R-squared for the LMM with each of these characteristics. The proposed R-squared measures the proportion of generalized variance explained by ?xed predictors in the model. Simulated and real longitudinal data are used to illustrate the statistical properties of the proposed R-squared and its capacity to assist analysts with covariance model selection and assessment of model goodness-of-fit.