Multinomial logit random effects models

Jonathan Hartzel, Alan Agresti, Brian Caffo

Research output: Contribution to journalArticlepeer-review

113 Scopus citations


This article presents a general approach for logit random effects modelling of clustered ordinal and nominal responses. We review multinomial logit random effects models in a unified form as multivariate generalized linear mixed models. Maximum likelihood estimation utilizes adaptive Gauss-Hermite quadrature within a quasi-Newton maximization algorithm. For cases in which this is computationally infeasible, we generalize a Monte Carlo EM algorithm. We also generalize a pseudo-likelihood approach that is simpler but provides poorer approximations for the likelihood. Besides the usual normality structure for random effects, we also present a semi-parametric approach treating the random effects in a non-parametric manner. An example comparing reviews of movie critics uses adjacent-categories logit models and a related baseline-category logit model.

Original languageEnglish (US)
Pages (from-to)81-102
Number of pages22
JournalStatistical Modeling
Issue number2
StatePublished - Jul 2001
Externally publishedYes


  • adjacent-categories logit
  • baseline-category logit
  • generalized linear mixed model
  • nominal variable
  • non-parametric maximum likelihood
  • ordinal variable
  • quasi symmetry

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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