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I have 3 correlations between A and B through 3 different studies :

   data :

   study   n     r      
       1  54  0,16      
       2  38  0,60      
       3  33  0,59      

But I would like to do a meta-analysis controlling for a 3rd factor C.

I did not a find a way to do it, is there any package available for this?

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There seem to be two questions that you are asking (one implicit question, and one explicit question):

  1. Can you meta-analyze the association between variable A and B, while controlling for the influence of variable C (implicit)
  2. What package (for R, I'm assuming) can you use to fit this meta-analytic model

Question 1:

Yes, you should be able to meta-analyze the association between variables A and B while controlling for C, if a few conditions are met.

We often think of correlations as the effect size of choice to meta-analyze the association between two variables, but all you need to conduct a meta-analysis are effect sizes, and their variances (or standard errors). Regression weights are effect sizes, and their standard errors are typically outputted in most statistical software, so you could meta-analyze the regression weights of A predicting B from models (based on your three studies) in which B is regressed on both A and C.***

The caveat is that you need to ensure these regression models are comparable--this is the primary reason why most regression parameters get excluded from meta-analyses, because different models control for different variables, or the variables are scaled differently. So as long as:

  • You only meta-analyze regression weights from models with the same groups of predictors AND
  • Each of those variables is scaled the same way from study-to-study (so that their unstandardized regression estimates "mean" the same thing)

Then you should be able to get a meta-analytic estimate of the association between A and B while controlling for C.

*** Alternatively, you could meta-analyze the regression weight of B prediction A, from a model in which A is regressed on both B and C.

Question 2

This question isn't really on point for CrossValidated (supposed to be more about conceptual understanding than programming) but all of the meta-analysis packages for R that I'm aware of (e.g., metafor, metaSEM) can readily synthesize this kind of data, as long as you supply the functions with effect size and precision (effect size variance or standard error) data.

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