[R-sig-ME] Variance of the fixed effects lme4

[Paul Johnson]

Hi Simon,

The usual way is to calculate the variance of the fitted values on the link scale, using only the fixed effects. 
E.g. for lme4 fits, appendix S6 of https://doi.org/10.1098/rsif.2017.0213 gives:

# Calculation of the variance in fitted values
VarF <-var(as.vector(model.matrix(parmodGLMERf) %*% fixef(parmodGLMERf)))

Which is essentially the same as the method used in the code for the original Nakagawa & Schielzeth R2_GLMM paper cited in the website you mentioned: https://doi.org/10.1111/j.2041-210x.2012.00261.x

I think this will be the same as:
VarF <-var(fitted(parmodGLMERf))

But as a general method this might be less safe because I can never remember if all the fitted() methods give the link scale fitted values by default, and whether they ever include random effects.

Best wishes,
Paul


> On 26 Oct 2020, at 07:42, Simon Harmel <sim.harmel using gmail.com> wrote:
> 
> Hello All,
> 
> The below website talks about the use of "the variance of the fixed
> effects" in the computation of R-squared from a mixed model.
> 
> But what is "the variance of the fixed effects"? Is it the sum of
> the diagonal elements obtained from:   vcov(fitted_model)?
> 
> The website:
> https://www.theanalysisfactor.com/r-squared-for-mixed-effects-models/
> 
> 	[[alternative HTML version deleted]]
> 
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