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 journalArticle

10 Citations (Scopus)

Abstract

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
JournalBiometrics
Volume56
Issue number1
StatePublished - Mar 2000
Externally publishedYes

Fingerprint

Logistic Regression Model
Logistics
Overdispersion
Proportion
Logistic Models
Testing
Exponential functions
Beta-binomial Distribution
Binomial Distribution
developmental toxicity
Toxicology
Toxicity
econometrics
conceptus
Dose-response
Appeal
testing
toxicology
Logistic Regression
Econometrics

Keywords

  • 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

  • Agricultural and Biological Sciences(all)
  • Public Health, Environmental and Occupational Health
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Statistics and Probability

Cite this

Estimation and testing with overdispersed proportions using the beta- logistic regression model of Heckman and Willis. / Slaton, Terra L.; Piegorsch, Walter W; Durham, Stephen D.

In: Biometrics, Vol. 56, No. 1, 03.2000, p. 125-133.

Research output: Contribution to journalArticle

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