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.
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
metafor, while introducing his own
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.