Simulations for estimation of random effects and overall effect in three-level meta-analysis of standardized mean differences using constant and inverse-variance weights

TL;DR

This paper introduces new moment-based estimators for three-level meta-analysis of standardized mean differences, offering improved bias, coverage, and convergence over traditional REML/PL methods.

Contribution

The authors develop and evaluate novel moment-based estimators for variance components and overall effect in three-level meta-analysis, addressing limitations of existing inverse-variance methods.

Findings

New estimators show reduced bias and better coverage in simulations.

Proposed methods do not suffer from convergence issues common in REML/PL.

Simulation results favor the new estimators over traditional approaches.

Abstract

We consider a three-level meta-analysis of standardized mean differences. The standard method of estimation uses inverse-variance weights and REML/PL estimation of variance components for the random effects. We introduce new moment-based point and interval estimators for the two variance components and related estimators of the overall mean. Similar to traditional analysis of variance, our method is based on two conditional $Q$ statistics with effective-sample-size weights. We study, by simulation, bias and coverage of these new estimators. For comparison, we also study bias and coverage of the REML/PL-based approach as implemented in {\it rma.mv} in {\it metafor}. Our results demonstrate that the new methods are often considerably better and do not have convergence problems, which plague the standard analysis.