[R-meta] Egger-type test for multi-level meta-analysis

[Dr. Guido Schwarzer]

Hi all,

Another question on multi-level models (while I am still waiting for an answer on my previous one ;-) ).

I would like to conduct a test for small-study effects for data from a three-level model, e.g., for the dataset dat.konstantopoulos2011.

library("metafor")
library("metadat")
m.ml <- rma.mv(yi, vi, random = ~ 1 | district / school, data = dat.konstantopoulos2011)

If I understand James' comment from February 2018 correctly (https://stat.ethz.ch/pipermail/r-sig-meta-analysis/2018-February/000610.html), I could conduct an Egger-type test for small study effects by using cluster-robust variance estimation following a multi-level meta-regression with the standard error as moderator:

sse.ml <- update(m.ml, mods = sqrt(vi))
library("clubSandwich")
conf_int(sse.ml, vcov = "CR2")

Did I get this right?

Best wishes,
Guido