[R-meta] ML or REML in rma.mv

[Yefeng Yang]

Hey Tharaka,

Two points for your consideration:

1. ​Some simulation papers show that ML underestimates variance components, while REML does not. When sample sizes are not small, they should converge very well. Also, they do not show substantial discrepancy in the fixed effects estimation.

2. In the context of model selection, conventional wisdom thinks ML and REML matter a lot, because you can not directly compare likelihoods from REML models with different fixed effects. Interestingly, there is also simulation work indicating that using REML as an estimator for model selection is doable.

There are quite a few papers on the heterogeneity estimator in the context of meta-analysis. For example,

Viechtbauer W. Bias and efficiency of meta-analytic variance estimators in the random-effects model[J]. Journal of Educational and Behavioral Statistics, 2005, 30(3): 261-293.
Veroniki A A, Jackson D, Viechtbauer W, et al. Methods to estimate the between‐study variance and its uncertainty in meta‐analysis[J]. Research synthesis methods, 2016, 7(1): 55-79.
Petropoulou M, Mavridis D. A comparison of 20 heterogeneity variance estimators in statistical synthesis of results from studies: a simulation study[J]. Statistics in medicine, 2017, 36(27): 4266-4280.
Langan D, Higgins J P T, Jackson D, et al. A comparison of heterogeneity variance estimators in simulated random‐effects meta‐analyses[J]. Research synthesis methods, 2019, 10(1): 83-98.

Regards,
Yefeng
________________________________
From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> on behalf of Tharaka S. Priyadarshana via R-sig-meta-analysis <r-sig-meta-analysis using r-project.org>
Sent: 14 December 2023 8:16
To: r-sig-meta-analysis using r-project.org <r-sig-meta-analysis using r-project.org>
Cc: Tharaka S. Priyadarshana <tharakas.priyadarshana using gmail.com>
Subject: [R-meta] ML or REML in rma.mv

Hello everyone,

I recently came across a paper that used "ML" estimation for a multi-level
meta-analysis, i.e. using "ML" with "rma.mv" function.

According to "metafor" description, it says that, "use of restricted
maximum likelihood (REML) estimation is generally recommended";
https://wviechtb.github.io/metafor/reference/misc-recs.html#:~:text=When%20fitting%20models%20with%20the,method%3D%22REML%22%20
).

Could someone please explain to me whether is it possible to get
different results if someone uses "ML" estimation instead of "REML" with ""
rma.mv" function? If yes/no, why is that?
Then, what are the major issues if "ML" estimation is used instead of
"REML" with ""rma.mv" function?
Could you please also share if you have any references (or any other
examples) that discuss these points? I mean the use of "ML" or "REML"
estimation in multi-level meta-analytic models.

Thank you very much.

Best regards,
Tharaka

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