[R-meta] Multivariate multi-level meta-analysis: adjusting control variables when modeling publication bias?

[Viechtbauer, Wolfgang (NP)]

Hi Daniel,

Didn't you ask the same question here?

https://stats.stackexchange.com/q/633046/1934

Please see my answer there.

Best,
Wolfgang

> -----Original Message-----
> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
> Of Daniel Foster via R-sig-meta-analysis
> Sent: Tuesday, December 5, 2023 20:09
> To: r-sig-meta-analysis using r-project.org
> Cc: Daniel Foster <daniel.foster567 using gmail.com>
> Subject: [R-meta] Multivariate multi-level meta-analysis: adjusting control
> variables when modeling publication bias?
>
> Hello Wolfgang and all,
>
> I am carrying out multivariate multilevel meta-analysis using the
> rma.mv function in the metafor package, and I have come across an
> issue that has been giving me a lot of trouble. At this point I am at
> a stand still and any insight would be greatly appreciated!!
>
> When testing for publication bias using the PET approach, Doucouliagos
> & Stanley (2009), suggest using the following model in a weighted
> least squares formula:
>
> ES= B1(1/SE) + SIGMA ak(Zj/SEi )+ e
>
> Where SE is the standard error of the effect estimate,  Z is a vector
> of meta-independent variables reflecting differences across studies
> for the jth study in literature, ak is the meta-regression coefficient
> which reflects the effect of particular study characteristics.
>
> My confusion lies in the fact that they are suggesting that the
> control variables (Z) included need to be divided by the standard
> error of the effect estimate. My questions are this:
>
> Should I be dividing my control variables by the standard error of
> the effect estimate when using the rma.mv function?  I have found some
> multivariate multilevel meta-analyses that follow this method
> (Klomp, 2009), but then others that don't (at least explicitly;
> Akgunduz, 2018)
>
> If I do need to do this, it is not clear to me how a binary control
> variable can be incorporated in my mra.mv model (i.e., 1, 0). To my
> mind, it seems strange to divide a dichotomous variable by a
> continuous variable. What steps do I need to execute to include these
> variables in my mra.mv model?
>
> Thank you so much in advance for your insights!
>
> Daniel
>
> Akgunduz, Y. E., & Plantenga, J. (2018). doi: 10.1111/joes.12192
> Doucouliagos, H., & Stanley, T. D. (2009). doi: 10.1111/j.1467-8543.2009.00723.x
> Klomp, J., & De Haan, J. (2010). doi: 10.1111/j.1467-6419.2009.00597.x