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Coefficients of Determination for Mixed-Effects Models

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  • Dabao Zhang

    (Purdue University)

Abstract

The coefficient of determination is well defined for linear models and its extension is long wanted for mixed-effects models in agricultural, biological, and ecological research. We revisit its extension to define measures for proportions of variation explained by the whole model, fixed effects only, and random effects only. We propose to calculate unexplained variations conditional on individual random and/or fixed effects so as to keep individual heterogeneity brought by available predictors. While these measures were naturally defined for linear mixed models, they can be defined for a generalized linear mixed model using a distance measured along its variance function, accounting for its heteroscedasticity. We demonstrate the promising performance and utility of our proposed methods via simulation studies as well as applications to real data sets in agricultural and ecological studies.

Suggested Citation

  • Dabao Zhang, 2022. "Coefficients of Determination for Mixed-Effects Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 674-689, December.
    • Handle: RePEc:spr:jagbes:v:27:y:2022:i:4:d:10.1007_s13253-022-00507-0
    DOI: 10.1007/s13253-022-00507-0
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    References listed on IDEAS

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    1. Byron C. Jaeger & Lloyd J. Edwards & Kalyan Das & Pranab K. Sen, 2017. "An statistic for fixed effects in the generalized linear mixed model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(6), pages 1086-1105, April.
    2. Colin Cameron, A. & Windmeijer, Frank A. G., 1997. "An R-squared measure of goodness of fit for some common nonlinear regression models," Journal of Econometrics, Elsevier, vol. 77(2), pages 329-342, April.
    3. Byron C. Jaeger & Lloyd J. Edwards & Matthew J. Gurka, 2019. "An R2 statistic for covariance model selection in the linear mixed model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(1), pages 164-184, January.
    4. Dabao Zhang, 2017. "A Coefficient of Determination for Generalized Linear Models," The American Statistician, Taylor & Francis Journals, vol. 71(4), pages 310-316, October.
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