The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded

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
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 > Institute of Biodiversity Animal Health and Comparative 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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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
627871Social, economic and environmental drivers of zoonoses in Tanzania (SEEDZ)Sarah CleavelandBiotechnology and Biological Sciences Research Council (BBSRC)BB/L018926/1RI BIODIVERSITY ANIMAL HEALTH & COMPMED