-----Original Message-----
From: Hanel, Paul H P [mailto:p.hanel at essex.ac.uk]
Sent: Wednesday, 07 June, 2023 12:12
To: R Special Interest Group for Meta-Analysis
Cc: Viechtbauer, Wolfgang (NP)
Subject: RE: Meta-analysis of R^2 Values
Dear Wolfgang,
Thank you for making it possible to meta-analyse R-square values. Based on your
documentation I take you are referring to the standard R-square values, not the
adjusted one?
By entering the number of predictors mi, is your function computing the adjusted
R-square values? If so, how would you run a meta-analysis with the adjusted R-
squares?
Thank you
Paul
PS: I am happy to share the dataset with R-square values I am currently working
on as soon as its finalised.
-----Original Message-----
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces at r-project.org> On Behalf
Of Viechtbauer, Wolfgang (NP) via R-sig-meta-analysis
Sent: 01 June 2023 13:51
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-
project.org>
Cc: Viechtbauer, Wolfgang (NP) <wolfgang.viechtbauer at maastrichtuniversity.nl>
Subject: [R-meta] Meta-analysis of R^2 Values
Hi all,
On a number of occasions, the question has been raised on this mailing list
whether it is possible to meta-analyze R^2 values (I have also received this
question a number of times via email). See, for example:
https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2021-March/002708.html
https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2023-January/004325.html
https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2023-April/004554.html
In these discussions, valid concerns about this have been raised. For example,
R^2 values are 'directionless' (in contrast to the more commonly used outcome
measures used for meta-analyses, where positive and negative values can cancel
each other out). The question is also how to compute the sampling variance of R^2
values and whether some kind of transformation may be needed (to normalize the
sampling distribution).
I share (and raised some of) these concerns but I would also say that it is not
inherently wrong to meta-analyze R^2 values. Therefore, after a bit of further
reading, thinking, and running some simulations, I have now implemented measures
"R2" and "ZR2" in escalc(). The former is for raw R^2 values, although it should
be better to use the latter as it uses a variance-stabilizing transformation of
R^2 that also has normalizing properties (similar to the well-known r-to-z
transformation for raw correlation coefficients). You can find the documentation
about this here:
https://wviechtb.github.io/metafor/reference/escalc.html
(if you search for 'R-squared', you will find the right place in this ever
growing help page).
Some of the caveats / limitations are also mentioned there (e.g., the equations
assume that we are in a multivariate normal setting and that the true R^2 values
are non-zero).
If you want to try this out, first install the 'devel' version of metafor:
install.packages("remotes")
remotes::install_github("wviechtb/metafor")
and then this will work:
library(metafor)
dat <- dat.aloe2013
par(mfrow=c(2,1))
dat <- escalc(measure="R2", r2i=R2, mi=preds, ni=n, data=dat, slab=study) res <-
rma(yi, vi, data=dat) res forest(res, header=TRUE, xlim=c(-0.6,1.4), alim=c(0,1),
refline=coef(res), efac=2) title(expression(bold("Using Raw " * R^2 * "
Values")))
dat <- escalc(measure="ZR2", r2i=R2, mi=preds, ni=n, data=dat, slab=study) res <-
rma(yi, vi, data=dat) res pred <- predict(res, transf=transf.ztor2) pred
forest(res, header=TRUE, xlim=c(-0.6,1.4), alim=c(0,1), transf=transf.ztor2,
refline=pred$pred, efac=2) title(expression(bold("Using z-transformed " * R^2 * "
Values (back-transformed)")))
I cannot say whether a meta-analysis of the R^2 values for this particular
dataset is sensible. Just using it for illustration purposes.
If somebody has a dataset with R^2 values where they have a legitimate reason for
such a meta-analysis, I would love to hear about it. Any feedback in general is
of course welcome.
Best,
Wolfgang