[R-meta] Recommendations on quantifying heterogeneity in three-level meta-regression

Jens Schüler jens.schueler at wiwi.uni-kl.de
Thu Nov 16 14:25:46 CET 2017

Dear all,


I am currently working on a three-level meta-regression and I am a bit
unsure about how to properly/adequately report heterogeneity in such
mixed-effect models (whereas it is pretty clear cut for regular „two-level“
meta-regressions e.g. the recent best practice recommendations of
Gonzalez-Mule & Aguinis 2017


Currently the metafor rma.mv function provides us with variance estimates
for both levels and a Q-test on residual heterogeneity. Moreover, we are
provided with code on how to calculate I2 in multilevel models, which I did


Turning towards the metaSEM package of Cheung, he reports variance estimates
(no predictors vs. predictors) for both levels and R2
l-1-type-as-a-covariate). However, not I2. In his book (Cheung 2015)
reports, on page 186, some formulas on how to calculate I2 and ICC in
three-level models but ends with a cautionary note that we lack further
insight in order to make reliable statements on that matter.


Hence, I am a bit left in the dark in terms of what is currently appropriate
(or how to defend such choices) and would like to pick your brains on that



Best regards


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