[R-meta] Metafor results tau^2 and R^2

Hi Wolfgang,

Yes. I had read the Higgins 2002 paper a long time ago and knew that
there was an R^2, but had forgotten how this was defined and what it
meant. And *just because of that* my mistake arose:

   * R^2 is given by metafor next to I^2 and H^2 (by the way: who knows H^2?)
   * R^2 was 1 in the given example (and not larger)
   * I (probably like many others) didn't know Raudenbush's R^2.

There are simply too many R^2s around (and too few letters in the
alphabet ...).

Best,

Gerta

Am 10.08.2020 um 12:20 schrieb Viechtbauer, Wolfgang (SP):

Hi Gerta,

I would have figured the description in the parentheses (amount of heterogeneity accounted for) makes it clear that this is not the "R^2" from Higgins et al. (2002). help(print.rma) also documents the meaning of R^2 in the output. I wonder how many people actually know the "Higgins' R^2", given that I^2 has pretty much come out as the 'winner' from the 2002 paper that everybody reports.

Best,
Wolfgang

-----Original Message-----
From: Dr. Gerta R?cker [mailto:ruecker at imbi.uni-freiburg.de]
Sent: Sunday, 09 August, 2020 16:20
To: Viechtbauer, Wolfgang (SP); Dustin Lee; r-sig-meta-analysis at r-
project.org
Subject: Re: [R-meta] Metafor results tau^2 and R^2

Dear Wolfgang,

Thank you for clarifying this. I really thought it was the Higgins R^2,
as it stands in the neighborhood of I^2 and H^2 and also as in the given
case also its value 1 is plausible (however, in fact , Higgins's R^2
would not be expressed in percent).

I confused these two R^2s, and I might not be the only person confusing
these. Do you see a way to avoid this misconception, for example by
mentioning Raudenbush in the output text?

Best,

Gerta

Am 09.08.2020 um 12:57 schrieb Viechtbauer, Wolfgang (SP):

Hi All,

R^2 in the output of metafor is *not* R^2 from Higgins et al. (2002). It

is in fact a (pseudo) coefficient of determination that goes back to
Raudenbush (1994). It estimates how much of the (total) heterogeneity is
accounted for by the moderator(s) included in the model. If the *residual*
amount of heterogeneity (i.e., the unaccounted for heterogeneity) is 0 after
including the moderator(s) in the model, then R^2 is going to be 100% (i.e.,
all of the heterogeneity has been accounted for). One would in fact expect
then that the moderator (or set of moderators) is significant -- it would
actually be a bit odd if a moderator accounts for all of the heterogeneity,
but fails to be significant (although one could probably construct an
example where this is the case). And reporting R^2 is definitely useful,
although should be cautiously interpreted given that R^2 can be rather
inaccurate when k is small (as discussed in L?pez?L?pez et al., 2014).

Best,
Wolfgang