Conditional inference functions for mixed-effects models with unspecified random-effects distribution

Peng Wang, Guei Feng Tsai, Annie Qu

Research output: Contribution to journalArticlepeer-review


In longitudinal studies, mixed-effects models are important for addressing subject-specific effects. However, most existing approaches assume a normal distribution for the random effects, and this could affect the bias and efficiency of the fixed-effects estimator. Even in cases where the estimation of the fixed effects is robust with a misspecified distribution of the random effects, the estimation of the random effects could be invalid. We propose a new approach to estimate fixed and random effects using conditional quadratic inference functions (QIFs). The new approach does not require the specification of likelihood functions or a normality assumption for random effects. It can also accommodate serial correlation between observations within the same cluster, in addition to mixed-effects modeling. Other advantages include not requiring the estimation of the unknown variance components associated with the random effects, or the nuisance parameters associated with the working correlations. We establish asymptotic results for the fixed-effect parameter estimators that do not rely on the consistency of the random-effect estimators. Real data examples and simulations are used to compare the new approach with the penalized quasi-likelihood (PQL) approach, and SAS GLIMMIX and nonlinear mixed-effects model (NLMIXED) procedures. Supplemental materials including technical details are available online.

Original languageEnglish (US)
Pages (from-to)725-736
Number of pages12
JournalJournal of the American Statistical Association
Issue number498
StatePublished - 2012


  • Conditional score
  • Generalized estimating equation
  • Generalized linear mixed-effects model
  • Penalized generalized weighted least square
  • Penalized quasi-likelihood
  • Quadratic inference function

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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