A unifying framework for marginalised random-intercept models of correlated binary outcomes

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Abstract

We demonstrate that many current approaches for marginal modelling of correlated binary outcomes produce likelihoods that are equivalent to the copula-based models herein. These general copula models of underlying latent threshold random variables yield likelihood-based models for marginal fixed effects estimation and interpretation in the analysis of correlated binary data with exchangeable correlation structures. Moreover, we propose a nomenclature and set of model relationships that substantially elucidates the complex area of marginalised random-intercept models for binary data. A diverse collection of didactic mathematical and numerical examples are given to illustrate concepts.

Original languageEnglish (US)
Pages (from-to)275-295
Number of pages21
JournalInternational Statistical Review
Volume82
Issue number2
DOIs
StatePublished - Aug 2014

Keywords

  • Binary outcomes
  • Copulas
  • Marginal likelihood
  • Multivariate logit
  • Multivariate probit

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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