I have a data set that I'm going to use for a meta-analysis that has a lot of dependencies between the effect sizes. Because of this, I've started to look into how people normally handle this, resulting in me finding a couple of articles (e.g. Konstantopoulos 2010; Cheung 2014) about three-level meta-analyses.

However, what puzzles me with all of these articles is that they're always talking about three-level meta-analyses rather than starting from the more general n-level meta-analyses. For my data set, I have what probably would count as a four-level structure (effect sizes clustered in testing occasions; testing occasions clustered into samples of participants; and samples of participants clustered into published papers) but I never find any examples of this in the literature. As of now, I'm shifting the unit of analysis by creating grand means on the sample level (meaning that I have several effect sizes for the same sample, corresponding to different factors of the certain moderator I'm interested in for the time being), and then I apply some kind of three-level analysis on that data, but I've never seen any examples of this in the literature either.

Am I missing something here?


  • Cheung (2014). Modeling dependent effect sizes with three-level meta-analyses: a structural equation modeling approach. Psychological Methods, 2, 211-229.
  • Konstantopoulos (2011). Fixed effects and variance components estimation in three-level meta-analysis. Research Synthesis Methods, 2, 61-76.
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    $\begingroup$ You can fit multilevel models with as many levels as you deem suitable for your data with rma.mv() in the metafor package in R. $\endgroup$
    – Wolfgang
    May 18, 2016 at 17:58

1 Answer 1


Since the multi-level meta-analytic models are special cases of the more general multi-level models then it must be possible to fit them. People have only recently started to publish articles about multi-level models in meta-analysis so I suspect the answer to your question lies in the fact that to need such a model and to be able to fit it demands a large number of primary studies and in many fields of scientific enquiry this is rare.

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    $\begingroup$ It may not be about the statistical theory. Substantive applications are usually lack behind methodological development. I have recently collaborated in a meta-analysis using a three-level meta-analysis where the three-level meta-analysis is clearly required in the data. The paper was declined for review by an editor because the paper was considered as "methodological" rather than "substantive." $\endgroup$ May 19, 2016 at 4:45
  • $\begingroup$ @MikeCheung and if you submit it to a statistical journal they will say it is not sufficiently statistical. The woes of being ahead of the curve. $\endgroup$
    – mdewey
    May 19, 2016 at 7:30

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