I'd like to learn more about the statistical techniques that one should use for a meta-regression. I'm interested in both general theory, as well as examining methodologies in R.

  • $\begingroup$ I wish you could explain what is meaning of meta-regression? Describe it in your own simpler way. $\endgroup$ Mar 20 '15 at 16:35
  • $\begingroup$ Using a regression to analyze other studies, where each of the other studies is in turn itself a regression analysis. en.wikipedia.org/wiki/Meta-regression $\endgroup$
    – orange1
    Mar 20 '15 at 18:37
  • $\begingroup$ meta-Analysis implicitly meta-analysis of regression coefficients here could be useful if you have had all the studies carried out with the same model and same or similar target population. I am not yet sure about the kind of problem you have in mind. This simply inhibits me to talk about theoretical things that may be in your thoughts. $\endgroup$ Mar 22 '15 at 15:34
  • $\begingroup$ Meta-regression is a special case of a generic random effects model. The nature of the data presents a few special concerns, but I'd advise learning the general before moving on to the specific. Otherwise you may make a mistake if you follow a cookbook approach that isn't tailored to your specific needs. $\endgroup$ Mar 26 '15 at 17:11

Echoing Subhash's suggestion, if you intend to meta-analyze regression weights, and eventually examine continuous moderators of those weights via meta-regression, you need to be sure the effect sizes (i.e., the regression weights) came from identical models. That is to say, the models for each effect size contained the exact same variables. As this kind of model consistency is rare--at least it is in my field--it seems much more common for people to meta-analyze zero-order correlation coefficients.

As for resources about techniques for carrying out meta-regression, most meta-analysis texts will provide good introductory coverage; Borenstein et al.'s (2009) book is a good choice, and I have also heard nice things about Schmidt & Hunter's (2014)if you're going to be meta-analyzing correlation coefficients in particular. Alternatively, Cheung's (2014) paper describes an SEM approach to meta-analysis/meta-regression that has unique benefits.

In terms of R packages, Cheung (2015) mentions some of those available, including meta, rmeta, mvmeta, metaLik, and metafor, while introducing his own metasem package. metafor is a great comprehensive meta-analysis package; you'll easily be able to fit fixed- random- and mixed-effect models (i.e., conducting meta-regression), test for publication bias, and create useful meta-analytic visualizations (e.g., forest and funnel plots). If, however, you want to meta-analyze dependent effect sizes (e.g., one sample may yield multiple effect sizes that you wish to include in your meta-analysis), then the metasem package is what I would recommend. It makes it easy to conduct meta-analysis and meta-regression--you will be able to specify moderators at both level 2 (e.g., varying within a sample) and at level 3 (e.g., varying between samples).


Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to meta-analysis. West Sussex, UK: Wiley.

Cheung, M. W. L. (2014). Modeling dependent effect sizes with three-level meta-analysis: A structural equation modeling approach. Psychological Methods, 19, 211-229.

Cheung, M. W. L. (2015). metaSEM: An R package for meta-analysis using structural equation modeling. Frontiers in Psychology, 5, 1521.

Schmidt, F. L., & Hunter, J. E. (2014). Methods of meta-analysis: Correcting error and bias in research findings (3rd Edition). London, UK: Sage.

  • $\begingroup$ I don't think that meta-regression necessarily involves meta-analyzing regression weights. It involves looking at predictors of any kind of effect size. $\endgroup$ Apr 27 '20 at 0:28
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    $\begingroup$ I wasn't trying to argue that meta-regression = meta-analyzing regression weights here (I agree with your characterization). Rather, in this post I was saying the complication of trying to quantitatively synthesize this kind of effect size in particular is ensuring effect size comparability in terms of model equivalency. If different studies used different measurement approach and covariates, then the meaning of each study's estimated slope will be different, and this will create a really complicated pattern of heterogeneity. $\endgroup$
    – jsakaluk
    Apr 28 '20 at 13:18
  • 1
    $\begingroup$ Ah, yes. Very true. $\endgroup$ Apr 28 '20 at 19:43

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