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

Sun, Aug 9, 2020 3:57 AM

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 L?pez?L?pez et al., 2014).

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org]
On Behalf Of Dr. Gerta R?cker
Sent: Saturday, 08 August, 2020 23:09
To: Dustin Lee; r-sig-meta-analysis at r-project.org
Subject: Re: [R-meta] Metafor results tau^2 and R^2

Dear Dustin,

The results you report show that in this analysis there was no
between-study heterogeneity found at all. As explained in the message,
all measures given are measures of heterogeneity, also R^2. You find all
definitions in Higgins JP, Thompson SG. Quantifying heterogeneity in a
meta-analysis. Stat Med. 2002;21(11):1539-1558. doi:10.1002/sim.1186.

R^2 should not be confused with the coefficient of determination (which
is also often denoted R^2). It is unusual to report the heterogeneity
measure R^2 in a study report; most authors would report tau, tau^2 or I^2.

See also R?cker G, Schwarzer G, Carpenter JR, Schumacher M. Undue
reliance on I(2) in assessing heterogeneity may mislead. /BMC Med Res
Methodol/. 2008;8:79. Published 2008 Nov 27. doi:10.1186/1471-2288-8-79.

Best,

Gerta

Am 08.08.2020 um 22:13 schrieb Dustin Lee:

Dear all,

I am currently conducting a meta regression in which we are examining the
role of temporal effects (year of study) in the relationship between
organizational attitudes and job performance. Using a mixed-effects model
using ML estimation, our analyses have thus far produced results that do
not appear to be irregular.

Our problem: With one relationship the analysis is showing the following:
tau^2 (estimated amount of residual heterogeneity):     0 (SE = 0.0152)
tau (square root of estimated tau^2 value):             0
I^2 (residual heterogeneity / unaccounted variability): 0.00%
H^2 (unaccounted variability / sampling variability):   1.00
R^2 (amount of heterogeneity accounted for):            100.00%

However, the significance of the effect of 'year of study' is significant
along with the omnibus Q_M statistic. While I inherently understand this

is

due to the way in which these values (R^2, tau^2, I^2, etc.) are

calculated

and that it may be due to the smaller than ideal sample size (k =32) as
suggested by L?pez?L?pez and colleagues (2014). I am unsure on how these
findings should be reported, particularly the 100% R^2 with the

significant

predictor 'year of study' result.

Thank you for any assistance you may be able to provide.

All the best,

Dustin

Reference:
L?pez?L?pez, J. A., Mar?n?Mart?nez, F., S?nchez?Meca, J., Van den
Noortgate, W., & Viechtbauer, W. (2014). Estimation of the predictive

power

of the model in mixed?effects meta?regression: A simulation study.

*British

Journal of Mathematical and Statistical Psychology*, *67*(1), 30-48.

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

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