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

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  • Demirhan, Haydar
  • Kalaylioglu, Zeynep

Abstract

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.

Suggested Citation

  • Demirhan, Haydar & Kalaylioglu, Zeynep, 2015. "Joint prior distributions for variance parameters in Bayesian analysis of normal hierarchical models," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 163-174.
  • Handle: RePEc:eee:jmvana:v:135:y:2015:i:c:p:163-174
    DOI: 10.1016/j.jmva.2014.12.013
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    References listed on IDEAS

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    1. Menegaki, Angeliki N., 2011. "Growth and renewable energy in Europe: A random effect model with evidence for neutrality hypothesis," Energy Economics, Elsevier, vol. 33(2), pages 257-263, March.
    2. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    3. Kent Kovacs, 2013. "An empirical examination of the location and timing of non-renewals in a farmland differential assessment program," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 50(1), pages 245-263, February.
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    Cited by:

    1. Maura Mezzetti & Daniele Borzelli & Andrea d’Avella, 2022. "A Bayesian approach to model individual differences and to partition individuals: case studies in growth and learning curves," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1245-1271, December.
    2. Yu-Fang Chien & Haiming Zhou & Timothy Hanson & Theodore Lystig, 2023. "Informative g -Priors for Mixed Models," Stats, MDPI, vol. 6(1), pages 1-23, January.

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