R^2 meaning in linear mixed-effects model
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The linear mixed-effect model class provides the Rsq property (ordinary and adjusted) which captures the proportion of variability in the response explained by the model. Is that the variability explained by fixed effects only or both by fixed and random effects? From the documentation I get the feeling that it's fixed effects only. How would I find the proportion of variability explained by the random effects?
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Rik
le 22 Mar 2021
This is one of the most basic goodness-of-fit parameters. It is so basic even Excel inculdes it when you plot a trendline.
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Michael
le 17 Juil 2023
Estimating an R^2 for a linear mixed effects model is non-trivial and is certainly not basic statistics - suitable measures have only relatively recently been developed. In SPSS, the Nakagawa pseudo-R^2 is calculated.
Refs:
Nakagawa, S & Schielzeth, H, 2013. A general and simple method for obtaining R2 from generalized linear mixed-effects models. Methods in Ecology and Evolution, 4(2), 133-142.
Johnson, PCD, 2014. Extension of Nakagawa & Schielzeth's R2GLMM to random slopes models. Methods in Ecology and Evolution, 5(9), 944-946.
Nakagawa, S, Johnson, PCD & 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, 20170213.
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