An adjusted coefficient of determination (R2) for generalized linear mixed models in one go

The coefficient of determination (R2) is a common measure of goodness of fit for linear models. Various proposals have been made for extension of this measure to generalized linear and mixed models. When the model has random effects or correlated residual effects, the observed responses are correlat...

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Vydáno v:Biometrical Journal Ročník 65; číslo 7; s. e2200290 - n/a
Hlavní autor: Piepho, Hans‐Peter
Médium: Journal Article
Jazyk:angličtina
Vydáno: Germany Wiley 01.10.2023
Wiley - VCH Verlag GmbH & Co. KGaA
Témata:
average semivariance
Bias
bias correction
Coefficients
Correlation
first‐order Taylor‐series approximation
Goodness of fit
heritability
Residual effects
Statistical models
variance explained
average semivariance
bias correction
variance explained
first-order Taylor-series approximation
heritability
ISSN:0323-3847, 1521-4036, 1521-4036
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Shrnutí:The coefficient of determination (R2) is a common measure of goodness of fit for linear models. Various proposals have been made for extension of this measure to generalized linear and mixed models. When the model has random effects or correlated residual effects, the observed responses are correlated. This paper proposes a new coefficient of determination for this setting that accounts for any such correlation. A key advantage of the proposed method is that it only requires the fit of the model under consideration, with no need to also fit a null model. Also, the approach entails a bias correction in the estimator assessing the variance explained by fixed effects. Three examples are used to illustrate new measure. A simulation shows that the proposed estimator of the new coefficient of determination has only minimal bias.
Bibliografie:ObjectType-Article-1
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ISSN:0323-3847
1521-4036
1521-4036
DOI:10.1002/bimj.202200290