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I am learning multilevel meta-analysis (or, three-level meta-analysis e.g., https://bookdown.org/MathiasHarrer/Doing_Meta_Analysis_in_R/mlma.html, and Three-Level Multilevel Meta-analysis: What exactly are the three levels? Multilevel vs. Multilevel SEM Approaches) and trying to deeply understand how this new relatively new approach fits into the more commonly used general meta-analysis (or two-level meta-analyses) in relation to weighting.

For the general meta-analysis model, I learned that there are two different models based on the effect size weighting: fixed-effects model and random-effects model, the former uses the inverse variance weighting of sampling variance and the latter uses the inverse variance weighting of sampling variance plus tau^2 (i.e., between-study variances).

When talking about multilevel meta-analysis models, I've personally never heard that people discuss a model being fixed-effects or random-effects. I realized that metafor does not allow us to specify a fixed-effects model when running multilevel meta-analysis (although we can choose ML or REML for method). So, I am wondering if multilevel meta-analysis is theoretically a random-effects model?

So, my question is, Can we also call multilevel meta-analysis models either (i) fixed-effects model or (ii) random-effects model, based on the approach of weighting?

I would appreciate it if I could hear any perspectives, or where I can further read into, and parts that I am not understanding correctly if any.

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