[R-meta] Questions regarding REML and FE models and R^2 calculation in metafor

Dear Nevo,

Please see my responses below.

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:

r-sig-meta-analysis-bounces at r-project.org] On

Behalf Of Nevo Sagi via R-sig-meta-analysis
Sent: Thursday, 04 May, 2023 11:09
To: r-sig-meta-analysis at r-project.org
Cc: Nevo Sagi
Subject: [R-meta] Questions regarding REML and FE models and R^2

calculation in

metafor

Dear list members,

I conducted a meta-analysis on the role of climate in mediating a specific
ecological process, using the *metafor *package in R.
This is actually a meta-regression, using the rma.mv function, with
*temperature *and *precipitation *as moderators, along with some other
moderators related to experimental design. I also use reference as a

random

effect ('random = ~1|*Reference'*), as some references include more than
one experiment.

*1. FE vs REML model:*
After reading Wolfgang Viechtbauer's blog post
<https://wviechtb.github.io/metafor/reference/misc-models.html> on the
differences between fixed-effects and random-effects models in the
*metafor *package, I decided to use the FE method, because the studies I
gathered are not a random sample of the population of hypothetical

studies.

Instead, the sample is biased by underrepresentation of some climates and
overrepresentation of others.
I wonder whether my interpretation of the difference between FE and REML
models is correct, and would like to get some feedback on it.

I don't think this is really a good reason for using a FE model, because
the underrepresentation of some climates and overrepresentation of others
will affect your results either way. The bigger question is if climate is
an important moderator, which you can examine via meta-regression.

*2. R^2 calculation:*
Reviewers of my manuscript required that I provide R-squared values for
each of the climate moderators.
Using the *metafor *package, only rma.uni models (where random variables
cannot be specified) provide R^2 estimation.
In a previous conversation in this mailing list, Wolfgang indicated that
pseudo-R^2 can be calculated based on the variance (sigma2) reported by
models including and excluding the moderator in question:
*(res0$sigma2 - res1$sigma2) / res0$sigma2*
*where 'res0' is the model without coefficients and 'res1' the model

with.*

I have two problems with this solution:
1. FE models do not provide variance components (sigma2). Therefore, the
pseudo R-squared can be calculated only for REML models. I guess this can
be explained by the nature of the models, which I don't fully understand.

Yes, this approach to calculating such pseudo-R^2 values only works in RE
models.

2. When using REML models and performing the above calculation, I get

weird

results. For example, one of the pseudo R^2 values was above 1. This

cannot

mean that the moderator explained more than 100% of the variance in the
effect size. How comparable is this pseudo R^2 for the standard R^2 of
simpler models?

This is mathematically impossible. (res0$sigma2 - res1$sigma2) /
res0$sigma2 is the same as 1 - res1$sigma2 / res0$sigma2 and the second
term cannot be negative, so the resulting value cannot be larger than 1.

To conclude, I will be glad to get feedback on both problems:
1. Should I use a random-effect or fixed-effect model?
2. How do I get a reliable R^2 or an alternative measure of goodness of

fit

for single-moderator models that include a random structure and a sampling
variance?

Thank you very much,

Nevo Sagi

--
Dr. Nevo Sagi

Prof. Dror Hawlena's Risk-Management Ecology Lab
Department of Ecology, Evolution & Behavior
The Alexander Silberman Institute of Life Sciences
The Hebrew University of Jerusalem
Edmond J. Safra Campus at Givat Ram, Jerusalem 9190401, Israel.