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

Gerta Ruecker ruecker @end|ng |rom |mb|@un|-|re|burg@de
Mon Aug 10 13:52:56 CEST 2020

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 ...).



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 Rücker [mailto:ruecker using imbi.uni-freiburg.de]
>> Sent: Sunday, 09 August, 2020 16:20
>> To: Viechtbauer, Wolfgang (SP); Dustin Lee; r-sig-meta-analysis using 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 López‐López et al., 2014).
>>> Best,
>>> Wolfgang


Dr. rer. nat. Gerta Rücker, Dipl.-Math.

Institute of Medical Biometry and Statistics,
Faculty of Medicine and Medical Center - University of Freiburg

Stefan-Meier-Str. 26, D-79104 Freiburg, Germany

Phone:    +49/761/203-6673
Fax:      +49/761/203-6680
Mail:     ruecker using imbi.uni-freiburg.de
Homepage: https://www.uniklinik-freiburg.de/imbi-en/employees.html?imbiuser=ruecker

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