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Can you recommend any reads/webpages that elaborates when and what estimator to use in random effects model when conducting a meta-analysis?

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The documentation for the metafor() package (Viechtbauer, 2010) in R provides some good suggestions, as metafor() includes 9 different methods of estimating random-effects models. Viechtbauer recommends the references below as good sources for getting up to speed on the ins-and-outs of each estimator, and I've updated to include the references recommended by the commenters below. I would start with Veroniki et al. (2016; open-access).

References

DerSimonian, R., & Kacker, R. (2007). Random-effects model for meta-analysis of clinical trials: An update. Contemporary Clinical Trials, 28, 105–114.

Langan, D., Higgins, J., & Simmonds, M. (2017). Comparative performance of heterogeneity variance estimators in meta‐analysis: a review of simulation studies. Research Synthesis Methods, 8(2), 181-198.

Raudenbush, S. W. (2009). Analyzing effect sizes: Random effects models. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The handbook of research synthesis and meta-analysis (2nd ed., pp. 295–315). New York: Russell Sage Foundation.

Veroniki, A. A., Jackson, D., Viechtbauer, W., Bender, R., Bowden, J., Knapp, G., ... & Salanti, G. (2016). Methods to estimate the between‐study variance and its uncertainty in meta‐analysis. Research Synthesis Methods, 7(1), 55-79.

Viechtbauer, W. (2005). Bias and efficiency of meta-analytic variance estimators in the random- effects model. Journal of Educational and Behavioral Statistics, 30, 261–293.

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1-48. URL: http://www.jstatsoft.org/v36/i03/

Viechtbauer, W., López-López, J. A., Sánchez-Meca, J., & Marín-Martínez, F. (2015). A comparison of procedures to test for moderators in mixed-effects meta-regression models. Psychological Methods, 20, 360–374.

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    $\begingroup$ Furthermore, there are two quite recent review articles published that recommend to use either the Paule-Mandel or restricted maximum likelihood estimator: Veroniki, A. A., et al. (2016). Methods to estimate the between-study variance and its uncertainty in meta-analysis. and Langan, D., Higgins, J. P. T., & Simmonds, M. (2016). Comparative performance of heterogeneity variance estimators in meta-analysis: A review of simulation studies. $\endgroup$ – User33 Jan 15 '18 at 7:32
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    $\begingroup$ Perhaps worth mentioning that the very comprehensive review by Veroniki et al is available under a Creative Commons licence DOI: 10.1002/jrsm.1164 whereas the other one is behind a paywall $\endgroup$ – mdewey Jan 15 '18 at 13:08
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    $\begingroup$ Thanks all--updated the response to include suggested readings by User33, and recommend the Veroniki et al. paper in particular given that (as mdewey points out) it is OA. $\endgroup$ – jsakaluk Jan 16 '18 at 4:48

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