Nakagawa, S., Johnson, P. C.D. and Schielzeth, H. (2017) The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded. Journal of the Royal Society: Interface, 14(134), 20170213. (doi: 10.1098/rsif.2017.0213) (PMID:28904005) (PMCID:PMC5636267)
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Abstract
The coefficient of determinationR2quantifies the proportion of varianceexplained by a statistical model and is an important summary statisticof biological interest. However, estimatingR2for generalized linear mixedmodels (GLMMs) remains challenging. We have previously introduced a ver-sion ofR2that we calledR2GLMMfor Poisson and binomial GLMMs, but notfor other distributional families. Similarly, we earlier discussed how to estimateintra-class correlation coefficients (ICCs) using Poisson and binomial GLMMs.Inthis paper, we generalize our methodsto allothernon-Gaussian distributions,in particular to negative binomial and gamma distributions that are commonlyused formodellingbiological data. Whileexpanding ourapproach,we highlighttwo useful concepts for biologists, Jensen’s inequality and the delta method,both of which help us in understanding the properties of GLMMs. Jensen’sinequality has important implications for biologically meaningful interpretationof GLMMs, whereas the delta method allows a general derivation of varianceassociated with non-Gaussian distributions. We also discuss some special con-siderations for binomial GLMMs with binary or proportion data. We illustratethe implementation of our extension by worked examples from the field of ecol-ogy and evolution in theRenvironment. However, our method can be usedacross disciplines and regardless of statistical environments.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Johnson, Dr Paul |
Authors: | Nakagawa, S., Johnson, P. C.D., and Schielzeth, H. |
College/School: | College of Medical Veterinary and Life Sciences > School of Biodiversity, One Health & Veterinary Medicine |
Journal Name: | Journal of the Royal Society: Interface |
Publisher: | The Royal Society |
ISSN: | 1742-5689 |
ISSN (Online): | 1742-5662 |
Published Online: | 13 September 2017 |
Copyright Holders: | Copyright © 2017 The Authors |
First Published: | First published in Journal of the Royal Society: Interface 14(134): 20170213 |
Publisher Policy: | Reproduced under a Creative Commons license |
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