Statistics in Biosciences

, Volume 7, Issue 1, pp 108–128

Double Penalized H-Likelihood for Selection of Fixed and Random Effects in Mixed Effects Models


DOI: 10.1007/s12561-013-9105-x

Cite this article as:
Xu, P., Wang, T., Zhu, H. et al. Stat Biosci (2015) 7: 108. doi:10.1007/s12561-013-9105-x


The goal of this paper is to develop a double penalized hierarchical likelihood (DPHL) with a modified Cholesky decomposition for simultaneously selecting fixed and random effects in mixed effects models. DPHL avoids the use of data likelihood, which usually involves a high-dimensional integral, to define an objective function for variable selection. The resulting DPHL-based estimator enjoys the oracle properties with no requirement on the convexity of loss function. Moreover, a two-stage algorithm is proposed to effectively implement this approach. An H-likelihood-based Bayesian information criterion (BIC) is developed for tuning parameter selection. Simulated data and a real data set are examined to illustrate the efficiency of the proposed method.


Mixed effects models Hierarchical likelihood Modified Cholesky decomposition Penalized likelihood Variable selection 

Copyright information

© International Chinese Statistical Association 2013

Authors and Affiliations

  1. 1.Department of MathematicsSoutheast UniversityNanjingChina
  2. 2.Department of MathematicsHong Kong Baptist UniversityHong KongChina
  3. 3.Department of BiostatisticsUniversity of North CarolinaChapel HillUSA

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