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

Michael Dewey ||@t@ @end|ng |rom dewey@myzen@co@uk
Mon Aug 10 14:20:16 CEST 2020

I suppose that, at the risk of cluttering up the output, both could be 
reported. Then we can spend a happy few hours answering questions on 
this list about what the difference is.


On 10/08/2020 12:52, Gerta Ruecker wrote:
> 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 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

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