Estimation and testing with overdispersed proportions using the beta- logistic regression model of Heckman and Willis

Terra L. Slaton, Walter W. Piegorsch, Stephen D. Durham

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Methods are presented for modeling dose-related effects in proportion data when extra-binomial variability is a concern. Motivation is taken from experiments in developmental toxicology, where similarity among conceptuses within a litter leads to intralitter correlations and to overdispersion in the observed proportions. Appeal is made to the well-known beta-binomial distribution to represent the overdispersion. From this, an exponential function of the linear predictor is used to model the dose-response relationship. The specification was introduced previously for econometric applications by Heckman and Willis; it induces a form of logistic regression for the mean response, together with a reciprocal biexponential model for the intralitter correlation. Large-sample, likelihood-based methods for estimating and testing the joint proportion-correlation response are studied. A developmental toxicity data set illustrates the methods.

Original languageEnglish (US)
Pages (from-to)125-133
Number of pages9
Issue number1
StatePublished - Mar 2000
Externally publishedYes


  • Beta-binomial distribution
  • Correlated binary data
  • Developmental toxicology
  • Extra-binomial variability
  • Hierarchical model
  • Intralitter correlation
  • Litter effect
  • Logistic regression
  • Overdispersion
  • Teratology

ASJC Scopus subject areas

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


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