R^2 meaning in linear mixed-effects model

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Katharina
Katharina 2021-3-22
编辑： Katharina 2023-7-17
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
Rik 2021-3-22
This is not a question about Matlab, but about statistics.
Katharina
Katharina 2021-3-22
If MATLAB offers the Rsq property, it should be specified in the documentation what the Rsq they provide stands for.

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Katharina
Katharina 2021-3-25
Ordinary Rsq = 1 - SSE / SST
SST is SSR + SSE
SSR = sum((F – mean(F)).^2)
SSE = sum((y – F).^2); SSR = sum((F – mean(F)).^2), where F is the fitted conditional response of the linear mixed-effects model. The conditional model has contributions from both fixed and random effects.
Therefore, MATLAB's Rsq calculation for linear mixed-effect model does take both fixed effects and random effects into account.

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Rik
Rik 2021-3-22
The information you seek should be available on the Wikipedia page for the R².
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
Michael 2023-7-17
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.
Katharina
Katharina 2023-7-17
编辑：Katharina 2023-7-17
Thank you so much! I'll check these out!

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