[R-meta] Differences in I^2 estimation between meta and metafor packages
m|kew|cheung @end|ng |rom gm@||@com
Wed May 15 02:48:11 CEST 2019
As a follow-up of the discussion, the metaSEM package implements these
definitions of the I^2 with the likelihood-based CIs on them.
summary( meta(y=yi, v=vi, data=Hox02, I2=c("I2q", "I2hm", "I2am"),
Heterogeneity indices (I2) and their 95% likelihood-based CIs:
lbound Estimate ubound
Intercept1: I2 (Q statistic) 0.27625 0.60780 0.6749
Intercept1: I2 (harmonic mean) 0.27713 0.60885 0.6766
Intercept1: I2 (arithmetic mean) 0.26209 0.59052 0.6431
A brief introduction is available here:
Mike W.L. Cheung Phone: (65) 6516-3702
Department of Psychology Fax: (65) 6773-1843
National University of Singapore
On Tue, May 14, 2019 at 6:26 PM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
> Good points. I wrote up that FAQ because this question comes up quite a
> bit, since (by default, that is, with REML estimation) metafor does deviate
> a bit from how I^2 is typically computed (i.e., with 100*(Q - (k-1))/Q), so
> users are sometimes surprised by this.
> And I fully agree that there isn't a *right* way of computing I^2, just
> different definitions. I actually find the way the 'typical' sampling
> variance is computed (which is implicitly used by both definitions) rather
> weird. Other definitions have been proposed (in particular, by
> Takkouche/Spiegelman/Crippa), such as:
> I^2 = tau^2 / (tau^2 + s^2), where s^2 = k/sum(wi), where wi=1/vi (i.e.,
> the haromic mean of the sampling variances)
> I^2 = 1/k sum(tau^2 / (vi + tau^2)).
> Those actually seem a bit more intuitive to me. The 'hetmeta' package
> provides those versions (called R_I and R_b).
> -----Original Message-----
> From: Guido Schwarzer [mailto:sc using imbi.uni-freiburg.de]
> Sent: Tuesday, 14 May, 2019 11:59
> To: Viechtbauer, Wolfgang (SP); Rushkin, Megan C;
> r-sig-meta-analysis using r-project.org
> Subject: Re: [R-meta] Differences in I^2 estimation between meta and
> metafor packages
> Am 13.05.19 um 10:45 schrieb Viechtbauer, Wolfgang (SP):
> > Hi Megan,
> > This is answered here:
> This website nicely describes the differences in the calculation of I2
> in metafor and meta. As this is written from the metafor perspective, I
> would like to describe why meta uses the "other" definition. ;-)
> Wolfgang mentions two advantages of the metafor implementation of I2:
> 1) "more general definition"
> 2) "values of I2 and H2 will be consistent with ... tau2"
> I agree that the metafor implementation is more general as one gets a
> different I2 value for each estimation method of tau2. However, the meta
> implementation is also based on a generalization (to the situation in
> which precisions differ between studies) - see section 3.3 in Higgins &
> Thompons (2002).
> On the other hand, while the metafor implementation guarantees
> consistent estimates for I2 and tau2, the meta implementation guarantees
> consistency of the I2 estimate and the test for heterogeneity (which -
> like I2 - is based on Q and the number of studies).
> In summary, one should know the differences in the estimation of I2
> between metafor and meta, however, there is (in my opinion) no clear
> Best wishes, Guido
> R-sig-meta-analysis mailing list
> R-sig-meta-analysis using r-project.org
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