# Including covariates in a multivariate multi-level meta-analysis

I am carrying out a multivariate multi-level meta-analysis, and I have a question regarding including moderator variables in the context of publication bias. Doucouliagos and Stanley (2009) recommend modelling 1/SE as an independent variable in an ordinary least squares regression to test for evidence of publication bias. In a random effects/mixed effects model, the formulation (using the rma.va function in R) would be as follows:

overalleffectPET <- rma.mv(yi, vi,
+ mods = ~ SE,
+ random = list(~ 1 | EffectSize_ID, ~ 1 | Study_ID),
+ tdist= TRUE, data=data)


However, the author also suggest dividing moderator variables by the SE of the effect estimates, and incorporating these newly computed values in the model as predictors. I have both binary and continuous moderator variables, and it is not clear to me how I would do this using the rma.mv function.

For instance, I have a binary moderator variables indicating martial status (0=not married; 1= married). Using rma.va, is it as simple as creating a new variable reflecting this computation (see formulation 1) and incorporating this new variable as a predictor in the model (see formulation 2).

(1) maritialstatusSE < - data$$MaritalStatus/data$$SE

(2) overalleffectPET <- rma.mv(yi, vi,
+ mods = ~ SE + maritialstatusSE,
+ random = list(~ 1 | EffectSize_ID, ~ 1 | Study_ID),
+ tdist= TRUE, data=data)


Doucouliagos, H., & Stanley, T. D. (2009). Publication selection bias in minimum‐wage research? A meta‐regression analysis. British Journal of Industrial Relations, 47(2), 406-428.https://doi.org/10.1111/j.1467-8543.2009.00723.x