Joint prior distributions for variance parameters in Bayesian analysis of normal hierarchical models

Date

2015-03-01

Author

Demirhan, Haydar
Kalaylıoğlu Akyıldız, Zeynep Işıl

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In random effect models, error variance (stage 1 variance) and scalar random effect variance components (stage 2 variances) are a priori modeled independently. Considering the intrinsic link between the stages 1 and 2 variance components and their interactive effect on the parameter draws in Gibbs sampling, we propose modeling the variances of the two stages a priori jointly in a multivariate fashion. We use random effects linear growth model for illustration and consider multivariate distributions to model the variance components jointly including the recently developed generalized multivariate log gamma (G-MVLG) distribution. We discuss these variance priors as well as the independent variance priors exercised in the literature in different aspects including noninformativeness and propriety of the associated posterior density. We show through an extensive simulation experiment that modeling the variance components of different stages multivariately results in better estimation properties for the response and random effect model parameters compared to independent modeling. We scrutinize the sensitivity of response model coefficient estimates to the parameters of considered noninformative variance priors and find that their full conditional expectations are insensitive to noninformative G-MVLG prior parameters. We apply independent and joint models for analysis of a real dataset and find that multivariate priors for variance components lead to better fitted hierarchical model than the univariate variance priors.

Subject Keywords

Hierarchical models, Multi-level models, Multivariate log gamma, Random coefficient, Random effect, Variance components, Hyperprior, Hyperparameter, Directional derivative, Sensitivity analysis

URI

https://hdl.handle.net/11511/49158

Journal

JOURNAL OF MULTIVARIATE ANALYSIS

DOI

https://doi.org/10.1016/j.jmva.2014.12.013

Collections

Department of Statistics, Article

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Citation Formats

H. Demirhan and Z. I. Kalaylıoğlu Akyıldız, “Joint prior distributions for variance parameters in Bayesian analysis of normal hierarchical models,” JOURNAL OF MULTIVARIATE ANALYSIS, pp. 163–174, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/49158.