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

d@iuedecke m@iii@g oii uke@de d@iuedecke m@iii@g oii uke@de
Fri Mar 22 19:31:51 CET 2019

```Ok, I did not address your point regarding interpretation directly, but it can be derived from the two code-lines at the end of my previous answer:

I'm not quite sure what "r.squaredGLMM()" calculates, I think it's similar to the r2()-function that is based on Nakagawa et al:

r2_marginal <- var.fixed / (var.fixed + var.random + var.residual)
r2_conditional <- (var.fixed + var.random) / (var.fixed + var.random + var.residual)

So the marginal r2 is the model's fixed effects variance divided by it's "total" variance, while the conditional r2 is the sum of fixed and random effects divided by the total variance. Quoted from Nakagawa et al.: "Marginal R2 is concerned with variance explained by fixed factors, and conditional R2 is concerned with variance explained by both fixed and random factors."

> Does this mean that my random effect (category, six levels) does only marginally contribute to the model fit

Yes, the results suggest this statement. You can also calculate the ICC, which is a similar and useful measure to investigate the variance of a model's random effects structure.

> and if so, was my choice to introduce this random effect justified?

I would not only rely on measures like r2 or icc to decide whether I would use a mixed model or not. Sometimes, the justification is just the design or theoretical consideration. And mixed models do no harm, so if you have some kind of clustering or grouping structure in your data, a mixed model is justified.

Best
Daniel

-----Ursprüngliche Nachricht-----
Von: R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> Im Auftrag von Tim Richter-Heitmann
Gesendet: Freitag, 22. März 2019 18:17
An: r-sig-mixed-models using r-project.org
Betreff: [R-sig-ME] R.square in Mixed Models

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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