Application of hierarchical linear models to meta-analysis: Study of the Monte Carlo simulation on the functioning of traditional and empirical-Bayes effect size

An empirical study and comparison is made of the functioning of the effect size proposed from the traditional meta-analytical points of view and the hierarchical linear models. These estimators are compared in bias, efficiency and robustness, via a Monte Carlo simulation. The results show the best behaviour of Empirical Bayes estimator (EB). This estimator shows a slightly biased behaviour compared with the traditional, although it is obviously more efficient and robust than the alternative traditionally used. Thus, it is empirically proved that the hierarchical linear models are an alternative to the traditional methods of meta-analytical synthesis.