[R-sig-ME] R.square in Mixed Models

[Ben Bolker]

On 2019-03-22 1:16 p.m., Tim Richter-Heitmann wrote:
> Dear List,
> 
> i have used mixed models (six groups, 30 observation each) to model
> ecological interactions of protists with their environments.
> 
> I liked my models very much, 

  we all do :-)

but a reviewer now asked me to give
> R.square to show the explained variance of each model. I have now read a
> bit on that topic, and realized that r2s in GLMMs have limited value.
> 
> I did not want to argue my way out this request (because reviewers
> sometimes do not like this), so i generated some values with the MuMin
> package:
> 
> r.squaredGLMM(finalfit.sand.1)
>            R2m       R2c
> [1,] 0.2716636 0.2824504
> 
> It is understoodd that the first value represents my fixed effects, and
> the second value the sum of fixed and random effects. My task is to now
> properly interpret these values. Does this mean that my random effect
> (category, six levels) does only marginally contribute to the model fit,
> and if so, was my choice to introduce this random effect justified?

  I would say "yes" (the random effect doesn't explain much additional
variance) and "yes" (it's an intrinsic aspect of the experimental
design; there's no point in taking it out.  Hurlbert 1984 would call
that "sacrificial pseudoreplication").

> 
> Thank you for taking your time.
>