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

Dr. Gerta Rücker ruecker @end|ng |rom |mb|@un|-|re|burg@de
Sat Aug 8 23:09:18 CEST 2020

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 Rücker 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.



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 López‐López 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:
> López‐López, J. A., Marín‐Martínez, F., Sánchez‐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.
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