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

[Uanhoro, James]

These R2 values have limited interpretations beyond the algebra that produced them; so sticking to an interpretation closest to the algebra is best: http://doi.wiley.com/10.1111/j.2041-210x.2012.00261.x.

Additionally, the choice of modeling random effects should probably not be based on the size of the random effect variance - there are additional considerations e.g., cluster sizes, see design effect formula. The best advice with these models is to model the data structure you have.

Others may have more problems with using random effects with a six-level grouping structure. But from a Bayesian perspective, this poses not so many problems; see brms package and suggestions in a paper by Andrew Gelman: http://projecteuclid.org/euclid.ba/1340371048.




On Mar 22 2019, at 1:16 pm, Tim Richter-Heitmann <trichter using uni-bremen.de> 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, 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?

Thank you for taking your time.

--
Dr. Tim Richter-Heitmann

University of Bremen
Microbial Ecophysiology Group (AG Friedrich)
FB02 - Biologie/Chemie
Leobener Straße (NW2 A2130)
D-28359 Bremen
Tel.: 0049(0)421 218-63062
Fax: 0049(0)421 218-63069

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