[R-meta] Choice of moderator for Egger's regression test in rma.mv

[Elizabeth Wade]

Dear all,

I have fit a three-level model using rma.mv to meta-analyze correlation
coefficients corrected for measurement unreliability. Based on this
documentation (
http://www.metafor-project.org/doku.php/tips:hunter_schmidt_method), I have
weighted the model using the inverse of the corrected variance.

My model is:
model <- rma.mv(ri.c, vi.c, W = 1/vi.c, random = ~ 1 |
Study_ID/Effect_ID, data = data, method = "REML")

Now I am intending to perform Egger's regression test. Based on this
explanation (
https://stats.stackexchange.com/questions/155693/metafor-package-bias-and-sensitivity-diagnostics),
I selected the inverse of the variance to use as a moderator in the
regression test.

So I have:
<http://www.metafor-project.org/doku.php/tips:hunter_schmidt_method>egger.model
<- rma.mv(ri.c, vi.c, W = 1/vi.c, mods = 1/vi.c, random = ~ 1 |
Study_ID/Effect_ID, data = data, method = "REML")

As I do this, I wonder whether it is appropriate to use the inverse
variance to both weight the model and to perform Egger's test. Will this
not detect publication bias, given that I am examining potential bias using
the same variable with which I weighted my model? Do you recommend a
different approach?

As an aside, I also wonder why some documentation uses the tilde before the
moderators are listed (mods = ~age) and some do not (mods = 1/vi.c).

Thank you for reading,
Betsy Wade

Betsy Wade, MA
Clinical Psychology Doctoral Student
Department of Psychology
University of Pennsylvania

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