A likelihood reformulation method in non-normal random effects models

Lei Liu*, Zhangsheng Yu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

58 Scopus citations


In this paper, we propose a practical computational method to obtain the maximum likelihood estimates (MLE) for mixed models with non-normal random effects. By simply multiplying and dividing a standard normal density, we reformulate the likelihood conditional on the non-normal random effects to that conditional on the normal random effects. Gaussian quadrature technique, conveniently implemented in SAS Proc NLMIXED, can then be used to carry out the estimation process. Our method substantially reduces computational time, while yielding similar estimates to the probability integral transformation method (J. Comput. Graphical Stat. 2006; 15:39-57). Furthermore, our method can be applied to more general situations, e.g. finite mixture random effects or correlated random effects from Clayton copula. Simulations and applications are presented to illustrate our method.

Original languageEnglish (US)
Pages (from-to)3105-3124
Number of pages20
JournalStatistics in Medicine
Issue number16
StatePublished - Jul 20 2008


  • Gamma frailty model
  • Gaussian copula
  • Generalized linear mixed model
  • Heterogeneity model
  • Logistic distribution

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


Dive into the research topics of 'A likelihood reformulation method in non-normal random effects models'. Together they form a unique fingerprint.

Cite this