[R-meta] variance explained by fixed & random effects

[Theresa Stratmann]

Dear Meta-Analysis Community,

I am using the metafor package to help me summarize some data on habitat selection. I have a question whose answer I have not found yet on the useful metafor website, and was hoping that someone could help me (or point me to an online resource I missed). 

As part of the description of my meta-analysis I would like to explain how much of the variation in habitat selection is due to my fixed effects (season) versus my random effects (individual & year). 

For a normal mixed-effects model I know how to compute the marginal and conditional R^2 (Nakagawa & Schielzeth 2013), but I am wondering how to do this correctly for a meta-analysis, or maybe, better said, talk about variance explained by the fixed and random effects. 

First I looked into I^2 and the post on this for random effect models. But then I read more from Borenstein et al. (https://www.meta-analysis-workshops.com/download/common-mistakes1.pdf) and was not quiet sure anymore if this is what I want (I^2 = proportion of observed variance that reflects variance in the true effects and not the sampling error ... so this seems more of a summary for the entire model (?), which also needs to be treated with care and presented properly). 

Then I found this question on this mailing list: https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2017-September/000232.html  ...but cannot really get this code to produce anything sensible, because I guess I am not clear on the formula for res0 vs. res1. 

So I will give a different example, which closely approximates what I am trying to do (a model with fixed & random effects): 

dat <- dat.konstantopoulos2011 
res <- rma.mv(yi, vi, mods = ~ factor(year), list( ~ 1 | district , ~ 1|school)  data=dat) 
res 

How would you calculate / correctly describe variance explained by the fixed effects (year)? By the random effects (district, school)? I am not tied to a particular statistic, just want to make sure that whatever I do is an honest representation of my results and gives readers (& myself) the information they need to interpret the results. 

I am new to meta-analyses and this is just a small part of my project, so I have been able to do some reading, but not an in-depth dive. Therefore I would appreciate any help you can offer.

Many thanks,

Theresa Stratmann 

B.S. Ecology, The University of Georgia 
M.S. Wildlife & Fisheries Biology, Clemson University 

PhD Student 
Goethe University 
and 
Senckenberg Biodiversity and Climate Research Center