# [R-meta] Metafor Fixed Effects giving I2- why?

Gerta Ruecker ruecker @end|ng |rom |mb|@un|-|re|burg@de
Tue Jul 30 10:37:22 CEST 2019

Hi all,

The question whether it is possible in the fixed effect model that tau^2
= 0 though I^2 > 0 was not answered in Wolfgang's reply. Following his
response, in this case metafor calculates

I^2 = (Q - (df)) / Q,

which probably means

I^2 = max(0, (Q - (df)) / Q).

Now it depends on the way tau^2 is calculated. For the DerSimonian-Laird
estimate, \hat tau^2 has the same numerator as I^2, that is, if \hat
tau^2 = 0, then I^2 = 0.

Thus the case Arthur describes can only, if at all, occur for other
tau^2 estimates. Thus, I repeat his question: Is it possible and under
which circumstances?

Best,

Gerta

Am 29.07.2019 um 19:56 schrieb Viechtbauer, Wolfgang (SP):
> Hi Arthur,
>
> Indeed, for random/mixed-effects models, I^2 is computed with tau^2 / (tau^2 + v), where tau^2 is the estimate of (residual) heterogeneity and v is the 'typical' sampling variance. So, if tau^2 = 0, then I^2 = 0.
>
> Since I^2 is a useful statistic also for fixed-effects models, I^2 is also computed then, but using (Q - (df)) / Q, where Q is the test statistic for (residual) heterogeneity and df = degrees of freedom of the test (k-1 for a model without moderators). But this has no effect on the rest of the computations (such as the weights).
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Aman Dheri
> Sent: Monday, 29 July, 2019 19:11
> To: r-sig-meta-analysis using r-project.org
> Subject: [R-meta] Metafor Fixed Effects giving I2- why?
>
> Hello,
>
> I am doing a fixed effects meta-analysis in Metafor and I see that it returns a non-zero I^2 value when tau^2 is always zero. According to Metafor documentation the fixed effects model in rma.uni should be 0 because of its calculation from the tau^2. Does any one know why this is happening, and if it is changing the weighting during the meta-analysis vs if the I^2 was 0?
>
> I assumed my code wasn’t needed for the answer to this but please let me know if I’m wrong!
>
> Thank you!
> Arthur
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--

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
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