Thanks again - this is exactly what I wanted to know (and thought the
original post referred to).
Gerta
Am 30.07.2019 um 16:31 schrieb Viechtbauer, Wolfgang (SP):
And yes, one can construct examples where the estimate of tau^2 = 0,
while I^2 > 0 (when I^2 is computed with max(0, (Q - (df)) / Q)). As you
pointed out, this can't happen when estimating tau^2 wit the DL estimator,
but it can happen when using other estimators. For example:
yi <- c(.2, .3, .4, .5)
vi <- rep(.0125, 4)
res <- rma(yi, vi, method="FE")
res$I2
rma(yi, vi, method="ML")$tau2 # this is essentially 0
var(yi)*3/4 - .0125 # for this case, ML reduces to this
(same goes for the HS estimator, which is identical to ML when the
sampling variances are homoscedastic; all other estimators should give an
estimate > 0)
Best,
Wolfgang
-----Original Message-----
From: Gerta Ruecker [mailto:ruecker at imbi.uni-freiburg.de]
Sent: Tuesday, 30 July, 2019 16:16
To: Viechtbauer, Wolfgang (SP); Aman Dheri;
r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] Metafor Fixed Effects giving I2- why?
Thank you, Wolfgang!
The difference is between the *parameter* tau^2, which is zero if we
believe the fixed effect model, and the estimate \hat tau^2, which in
your example is likewise positive (all methods), though (of course)
Best,
Gerta
Am 30.07.2019 um 15:28 schrieb Viechtbauer, Wolfgang (SP):
My understanding of Arthur's question was that he is wondering why the
following code yields a value of I^2 = 40% given that this fits a
fixed-effects model where tau^2 = 0 by definition.
library(metafor)
yi <- c(.2, .3, .4, .5)
vi <- rep(.01, 4)
res <- rma(yi, vi, method="FE")
res$I2
(and in the 'devel' version, the value of I^2 is shown explicitly in
the output also for a FE model).
Best,
Wolfgang
-----Original Message-----
From: Gerta Ruecker [mailto:ruecker at imbi.uni-freiburg.de]
Sent: Tuesday, 30 July, 2019 10:37
To: Viechtbauer, Wolfgang (SP); Aman Dheri;
r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] Metafor Fixed Effects giving I2- why?
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 at r-project.org] On Behalf Of Aman Dheri
Sent: Monday, 29 July, 2019 19:11
To: r-sig-meta-analysis at 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
--
Dr. rer. nat. Gerta R?cker, 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 at imbi.uni-freiburg.de
Homepage: https://www.imbi.uni-freiburg.de/persons/ruecker/person_view