Recommended readings
See the following texts for more information on meta regression:
Berkey, C. S., Hoaglin, D. C., Mosteller, F., and Colditz, G. A. 1995. A random-effects regression model for meta-analysis. Statistics in Medicine, 14, 395–411.
DerSimonian, R., and Laird, N. 1986. Meta-analysis of clinical trials. Clinical Controlled Trials, 7, 177-188.
Hedges, L. V. 1983. A random effects model for effect sizes. Psychological Bulletin, 93, 388-395.
Hunter, J. E., and Schmidt, F. L. 2004. Methods of meta-analysis: Correcting error and bias in research synthesis, 2nd ed. Thousand Oaks, CA: Sage.
Knapp, G., and Hartung, J. 2003. Improved tests for a random effects meta-regression with a single covariate. Statistics in Medicine, 22, 2693–2710.
Morris, C. N. 1983. Parametric empirical Bayes inference: Theory and applications. Journal of the American Statistical Association, 78, 47–55.
Raudenbush, S. W. 2009. Analyzing effect sizes: Random-effects models. In: Handbook of Research Synthesis and Meta-Analysis, H. Cooper, L. V. Hedges, and J. C. Valentine, eds. 2nd ed. 295–316. New York: Russell Sage Foundation.
Sidik, K., and Jonkman, J. N. 2005. A note on variance estimation in random effects meta-regression. Journal of Biopharmaceutical Statistics, 15, 823–838.
Thompson, S. G., and S. J. Sharp. 1999. Explaining heterogeneity in meta-analysis: A comparison of methods. Statistics in Medicine, 18, 2693–2708.
Viechtbauer, W., J. A. Lopez-Lopez, J. Sanchez-Meca, and F. Marin-Martınez. 2015. A comparison of procedures to test for moderators in mixed-effects meta-regression models. Psychological Methods, 20, 360–3.