Estimation Parameters of Dependence Meta-Analytic Model: New Techniques for the Hierarchical Bayesian Model

Dependence in meta-analytic models can happen due to the same collected data or from the same researchers. The hierarchical Bayesian linear model in a meta-analysis that allows dependence in effect sizes is investigated in this paper. The interested parameters on the hierarchical Bayesian linear dependence (HBLD) model which was developed using the Bayesian techniques will then be estimated. The joint posterior distribution of all parameters for the hierarchical Bayesian linear dependence (HBLD) model is obtained by applying the Gibbs sampling algorithm. Furthermore, in order to measure the robustness of the HBLD model, the sensitivity analysis is conducted using a different prior distribution on the model. This is carried out by applying the Metropolis within the Gibbs algorithm. The simulation study is performed for the estimation of all parameters in the model. The results show that the obtained estimated parameters are close to the true parameters, indicating the consistency of the parameters for the model. The model is also not sensitive because of the changing prior distribution which shows the robustness of the model. A case study, to assess the effects of native-language vocabulary aids on second language reading, is conducted successfully in testing the parameters of the models.