A coefficient of determination (R2) for generalized linear mixed models

Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R2) or the adjusted R2 are well established for linear models, it is not obvious how such measures should be defined for generalized linea...

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Bibliographic Details
Published in:Biometrical journal Vol. 61; no. 4; pp. 860 - 872
Main Author: Piepho, Hans‐Peter
Format: Journal Article
Language:English
Published: Germany Wiley - VCH Verlag GmbH & Co. KGaA 01.07.2019
Subjects:
Adolescent
Animals
Biological analysis
Biometry - methods
Child
Coleoptera
Covariance
Female
generalized linear mixed models
generalized linear models
Goodness of fit
Horseshoe Crabs
Humans
Larva
linear mixed models
Linear Models
Male
Models, Statistical
Multivariate Analysis
Nesting Behavior
Orthodontics
semivariogram
Statistical models
total variance
generalized linear models
semivariogram
total variance
generalized linear mixed models
goodness-of-fit
linear mixed models
ISSN:0323-3847, 1521-4036, 1521-4036
Online Access:Get full text
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Summary:Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R2) or the adjusted R2 are well established for linear models, it is not obvious how such measures should be defined for generalized linear and mixed models. There are by now several proposals but no consensus has yet emerged as to the best unified approach in these settings. In particular, it is an open question how to best account for heteroscedasticity and for covariance among observations present in residual error or induced by random effects. This paper proposes a new approach that addresses this issue and is universally applicable for arbitrary variance‐covariance structures including spatial models and repeated measures. It is exemplified using three biological examples.
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ISSN:0323-3847
1521-4036
1521-4036
DOI:10.1002/bimj.201800270