Statistics and Computing

, Volume 18, Issue 1, pp 1–13 | Cite as

Bayesian parsimonious covariance estimation for hierarchical linear mixed models

  • Sylvia Frühwirth-SchnatterEmail author
  • Regina Tüchler


We consider a non-centered parameterization of the standard random-effects model, which is based on the Cholesky decomposition of the variance-covariance matrix. The regression type structure of the non-centered parameterization allows us to use Bayesian variable selection methods for covariance selection. We search for a parsimonious variance-covariance matrix by identifying the non-zero elements of the Cholesky factors. With this method we are able to learn from the data for each effect whether it is random or not, and whether covariances among random effects are zero. An application in marketing shows a substantial reduction of the number of free elements in the variance-covariance matrix.


Covariance selection Random-effects models Markov chain Monte Carlo Fractional prior Variable selection 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Applied Statistics and EconometricsJohannes Kepler Universität LinzLinzAustria
  2. 2.Department of Statistics and MathematicsVienna University of Economics and Business AdministrationViennaAustria

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