Proportion of explained variance in a mixed-effects model I do not know if this has been asked before, but I do not found anything about it. My question is if anyone can provide a good reference to learn how to obtain the proportion of variance explained by each one of the fixed and random factors in a mixed-effects model.
 A: According to this blog post from 2013, the MuMIn package in R can provide R$^2$ values for mixed models ala an approach developed by Nakagawa & Schielzeth 2013$^1$ (which was mentioned in a previous answer).
#load packages
library(lme4)
library(MuMIn)

#Fit Model
m <- lmer(mpg ~ gear + disp + (1|cyl), data = mtcars)

#Determine R2:
r.squaredGLMM(m) 

       R2m       R2c 
 0.5476160 0.7150239  

The output for functionr.squaredGLMM provides:


*

*R2m: marginal R squared value associated with fixed effects

*R2c conditional R2 value associated with fixed effects plus the random effects. 
Note: a comment on the linked blog post suggests that an alternative Nakagawa & Schielzeth inspired approach developed by Jon Lefcheck (using the sem.model.fits function in the piecewiseSEM package) produced identical results.  [So you have options :p].


*

*I did not test this latter function, but I did test the r.squaredGLMM() function in the MuMIn package and so can attest that it is still functional today (2018).

*As for the validity of this approach, I leave reading  Nakagawa & Schielzeth (2013) (and follow-up article Johnson 2014$^2$) up to you. 

 1: Nakagawa, S., and 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. 
 2: Johnson, P. C. D. 2014 Extension of Nakagawa & Schielzeth’s R2GLMM to random slopes models. Methods in Ecology and Evolution 5: 44–946. 
A: I can provide some references:
Xu, R. (2003). Measuring explained variation in linear mixed effects models. Statistics in Medicine, 22, 3527-3541. DOI:10.1002/sim.1572
Edwards, L. J., Muller, K. E., Wolfinger, R. D., Qaqish, B. F., & Schabenberger, O. (2008). An $R^2$ statistic for fixed effects in the linear mixed model. Statistics in Medicine, 27, 6137-6157. DOI:10.1002/sim.3429
Hössjer, O. (2008). On the coefficient of determination for mixed regression models. Journal of Statistical Planning and Inference, 138, 3022-3038. DOI:10.1016/j.jspi.2007.11.010
Nakagawa, S., & Schielzeth, H. (2013). A general and simple method for obtaining $R^2$ from generalized linear mixed-effects models. Methods in Ecology and Evolution, 4, 133-142. DOI:10.1111/j.2041-210x.2012.00261.x
Happy reading!
