Bayesian analysis of meta-analytic models incorporating dependency: new approaches for the hierarchical Bayesian delta-splitting model

Junaidi; Darfiana Nur; Irene Hudson; Elizabeth Stojanovski

doi:10.1016/j.heliyon.2020.e04835

Bayesian analysis of meta-analytic models incorporating dependency: new approaches for the hierarchical Bayesian delta-splitting model

Heliyon. 2020 Sep 21;6(9):e04835. doi: 10.1016/j.heliyon.2020.e04835. eCollection 2020 Sep.

Authors

Junaidi¹, Darfiana Nur², Irene Hudson³, Elizabeth Stojanovski⁴

Affiliations

¹ Tadulako University, Palu 94118, Indonesia.
² Curtin University, Bentley WA 6102, Australia.
³ RMIT University, Melbourne VIC 3001, Australia.
⁴ Newcastle University, Callaghan, NSW 2308, Australia.

Abstract

Dependence between studies in meta-analysis is an assumption which is imposed on the structure of hierarchical Bayesian meta-analytic models. Dependence in meta-analysis can occur as a result of study reports using the same data or from the same authors. In this paper, the hierarchical Bayesian delta-splitting (HBDS) model (Steven and Taylor, 2009), which allows for dependence between studies and sub-studies by introducing dependency at the sampling and hierarchical levels, is developed using Bayesian approaches. Parameter estimation obtained from the joint posterior distributions of all parameters for the HBDS model was conducted using the Metropolis within Gibbs algorithm. The estimation of parameters for simulation studies using R code confirmed the consistency of the model parameters. These parameters were then tested successfully on studies to assess the effects of native-language vocabulary aids on second language reading as a case study.

Keywords: Computational mathematics; Dependence meta-analytic; Hierarchical Bayesian delta-splitting; Mathematics.