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Comment & Response
February 4, 2019

Reporting of R2 Statistics for Mixed-Effects Regression Models

Author Affiliations
  • 1Department of Neurology, Johns Hopkins University School of Medicine, Baltimore, Maryland
  • 2Department of Biostatistics, Johns Hopkins University, Baltimore, Maryland
JAMA Neurol. 2019;76(4):507. doi:10.1001/jamaneurol.2018.4720

To the Editor We read with interest the article by Andorra et al1 that evaluated the dynamics of brain volume loss in multiple sclerosis and modeled these variables in mixed-effects regression models as functions of disease duration. The authors report various goodness-of-fit measures of their models, focusing on the coefficient of determination (R2), which ranges from 0 to 1 and represents the proportion of variance in the dependent variable explained by the model. For a model such as ordinary least squares regression, which includes only fixed-effects components, the interpretation of the R2 is intuitive and represents the variance of the dependent variable explained by the independent variable(s). For mixed-effects regression models, there are several variance components, which include both fixed and random effects. Andorra et al1 cite methods developed by Nakagawa and Schielzeth2 in calculating their article’s R2 values. The methods of Nakagawa and Schielzeth define R2 statistics for mixed-effects models as follows: (1) marginal R2 (variance explained by only fixed effects) and (2) conditional R2 (variance explained by both fixed and random effects). The marginal R2 is consistent with how most readers will interpret an R2 statistic (using the traditional ordinary least squares interpretation). Notably, Nakagawa and Schielzeth recommend that both marginal and conditional R2 be reported given that they convey unique and distinctive information.