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

[Viechtbauer, Wolfgang (NP)]

Dear Nevo,

Please see my responses below.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using 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 using 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.