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Are there any suitable selection models of publication bias for multilevel meta-analyses?

I am currently conducting a 3-level meta-analysis and trying to incorporate selection models to assess publication bias. Of particular interest is Vevea and Woods'(2005) method. I used the weightr::weightfunct function for the Vevea and Woods method but I think it is only for traditional random effect models, thus not suitable for multilevel models (or is it?)

Thanks in advance.

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Unfortunately, there are not yet selection models that accommodate multilevel meta-analysis nor, indeed, many other forms of dependent or clustered effect sizes. This is an active area of research. A good review, with simulation results, on this topic is:

Rodgers, M. A., & Pustejovsky, J. E. (2021). Evaluating meta-analytic methods to detect selective reporting in the presence of dependent effect sizes. Psychological Methods, 26(2), 141.

This issue actually raises some fairly deep questions about what assumptions should be made on the selection process for a multilevel meta-analysis: for example, if papers contribute multiple point estimates, on which estimate(s) does selection operate? The estimate in the abstract? The average of all the estimates? Or...? There's still much work to be done.

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