, Volume 28, Issue 2, pp 543–564 | Cite as

A flexible class of parametric distributions for Bayesian linear mixed models

  • Mohsen Maleki
  • Darren WraithEmail author
  • Reinaldo B. Arellano-Valle
Original Paper


In this paper, we consider a linear mixed effect model (LMM) assuming that the random effect and error terms follow an unrestricted skew-normal generalized-hyperbolic (SUNGH) distribution. The SUNGH is a broad class of flexible distributions that includes various other well-known asymmetric and symmetric families and provides a high degree of flexibility for the modeling of complex multivariate data with different directions and degrees of asymmetry, kurtosis and heavy tails. The choice of the best fitting distribution can proceed quite naturally through parameter estimation or by placing constraints on specific parameters and assessing using model choice criteria. We estimate parameters of the LMM using a Bayesian approach and examine the performance of the proposed methodology on simulated and real data from a clinical trial on treatment options for schizophrenia (Lapierre et al. Acta Psychiatric Scandinavica 82:72–76, 1990; Ho and Lin Biom J 52(4):449–469, 2010).


Bayesian analysis Linear mixed effect model MCMC method Unrestricted skew-normal generalized-hyperbolic distribution Unrestricted skew-normal distribution 

Mathematics Subject Classification

62J02 62P10 62F15 



The authors would like to thank the AE and anonymous reviewers for their suggestions, corrections and encouragement, which helped us to improve earlier versions of the manuscript.


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Copyright information

© Sociedad de Estadística e Investigación Operativa 2018

Authors and Affiliations

  1. 1.Department of StatisticsShiraz UniversityShirazIran
  2. 2.Institute of Health and Biomedical Innovation (IHBI)Queensland University of Technology (QUT)BrisbaneAustralia
  3. 3.Department of StatisticsUniversidad Católica de ChileSantiagoChile

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