[R-meta] Egger's test with multilevel meta analysis

We have a paper (forthcoming in Psych Methods) evaluating a similar method
for adapting Egger's test to the multilevel context, using RVE:
* Rodgers, M. A., & Pustejovsky, J. E. (In Press). Evaluating Meta-Analytic
Methods to Detect Selective Reporting in the Presence of Dependent Effect
Sizes. Psychological Methods, forthcoming.
https://doi.org/10.31222/osf.io/vqp8u

There is also a related paper by Fernandez-Castilla and colleagues:
* Fern?ndez-Castilla, B., Declercq, L., Jamshidi, L., Beretvas, S. N.,
Onghena, P., & Van den Noortgate, W. (2019). Detecting selection bias in
meta-analyses with multipleoutcomes: A simulation study. The Journal of
Experimental Education, 1?20.

These tests can be implemented in rma.mv() simply by including the standard
error of the effect size (or a related measure of precision, such as the
sample size) as a moderator. Say that data includes a variable called sei
for the standard error of each effect size:

egger_multi <- rma.mv(yi = yi, V = sei^2, random = ~ 1 | studyID, effectID,
mods = ~ sei, data = dat)

Then apply cluster-robust standard errors for the RVE-based test:

coef_test(egger_multi, vcov = "CR2")

Further details available in our paper, and example code in our
supplementary materials.

James

[R-meta] Egger's test with multilevel meta analysis

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