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We consider six different estimators of residual heterogeneity in random-effects meta-regression, five estimators already known and implemented in the R package metafor and one estimator not yet considered in random-effects meta-regression. In a numerical study, we investigate the properties of these residual heterogeneity estimators as well as the impact of these estimators on the properties of the regression parameter estimates. It turns out that the new estimator performs quite well in terms of bias and mean squared error. The impact of the different residual heterogeneity estimators on the actual confidence coefficient of confidence intervals for regression parameters can be substantially different as shown in the numerical study.
Panityakul et al. (Tue,) studied this question.