Goodness-of-fit in generalized nonlinear mixed-effects models

Edward F. Vonesh*, Vernon M. Chinchilli, Kewei Pu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

182 Scopus citations


In recent years, generalized linear and nonlinear mixed-effects models have proved to be powerful tools for the analysis of unbalanced longitudinal data. To date, much of the work has focused on various methods for estimating and comparing the parameters of mixed-effects models. Very little work has been done in the area of model selection and goodness-of-fit, particularly with respect to the assumed variance covariance structure. In this paper, we present a goodness-of-fit statistic which can be used in a manner similar to the R2 criterion in linear regression for assessing the adequacy of an assumed mean and variance-covariance structure. In addition, we introduce an approximate pseudo-likelihood ratio test for testing the adequacy of the hypothesized covariance structure. These methods are illustrated and compared to the usual normal theory likelihood methods (Akaike's information criterion and the likelihood ratio test) using three examples. Simulation results indicate the pseudo-likelihood ratio test compares favorably with the standard normal theory likelihood ratio test, but both procedures are sensitive to departures from normality.

Original languageEnglish (US)
Pages (from-to)572-587
Number of pages16
Issue number2
StatePublished - Jun 1996


  • Concordance correlation
  • Longitudinal data
  • Mixed effects models
  • Pseudo- likelihood ratio test

ASJC Scopus subject areas

  • General Agricultural and Biological Sciences
  • Applied Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • Statistics and Probability


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