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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

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The reason why the authors divide everything by the SEs is that they are analyzing not effect size estimates as the outcome, but test statistics (which are in essence effect size estimates divided by their SEs). However, this is not how things work for random-effects models and models with a multilevel structure as you have. Here, you just include predictors in their original form.

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  • $\begingroup$ Thank you! To clarify, I am also carrying two other multilevel analyses - one uses the t-statistic as a dependent outcome, and another uses the partial correlation coefficient as the dependant outcome (the computation of which is derived from the t-statistic). You said the authors divide everything because they are working with test statistics, which makes me wonder whether the analyses I just mentioned require the same adjustment? However, you go on to say that random-effects models and models with a multilevel structure do not require this adjustment. Do you mind clarifying? $\endgroup$
    – Daniel
    Commented Dec 5, 2023 at 20:49

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