Flexible random intercept models for binary outcomes using mixtures of normals

Research output: Contribution to journalArticle


Random intercept models for binary data are useful tools for addressing between-subject heterogeneity. Unlike linear models, the non-linearity of link functions used for binary data force a distinction between marginal and conditional interpretations. This distinction is blurred in probit models with a normally distributed random intercept because the resulting model implies a probit marginal link as well. That is, this model is closed in the sense that the distribution associated with the marginal and conditional link functions and the random effect distribution are all of the same family. It is shown that the closure property is also attained when the distributions associated with the conditional and marginal link functions and the random effect distribution are mixtures of normals. The resulting flexible family of models is demonstrated to be related to several others present in the literature and can be used to synthesize several seemingly disparate modeling approaches. In addition, this family of models offers considerable computational benefits. A diverse series of examples is explored that illustrates the wide applicability of this approach.

Original languageEnglish (US)
Pages (from-to)5220-5235
Number of pages16
JournalComputational Statistics and Data Analysis
Issue number11
StatePublished - Jul 15 2007



  • Logit-normal
  • Marginalized multilevel models
  • Probit-normal

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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