Estimation and testing with overdispersed proportions using the beta-logistic regression model of Heckman and Willis |
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Authors: | Slaton T L Piegorsch W W Durham S D |
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Affiliation: | Department of Pharmacy, University of South Carolina, Columbia 29208, USA. |
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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. |
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Keywords: | Beta-binomial distribution Correlated binary data Developmental toxicology Extra-binomial variability Hierarchical model Intralitter correlation Litter effect Logistic regression Overdispersion Teratology |
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