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

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Mon Aug 10 12:20:59 CEST 2020

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.


>-----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-
>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?
>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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