### 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 language | English (US) |
---|---|

Pages (from-to) | 125-133 |

Number of pages | 9 |

Journal | Biometrics |

Volume | 56 |

Issue number | 1 |

State | Published - Mar 2000 |

Externally published | Yes |

### Fingerprint

### 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

*Biometrics*,

*56*(1), 125-133.

**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.

Research output: Contribution to journal › Article

*Biometrics*, vol. 56, no. 1, pp. 125-133.

}

TY - JOUR

T1 - Estimation and testing with overdispersed proportions using the beta- logistic regression model of Heckman and Willis

AU - Slaton, Terra L.

AU - Piegorsch, Walter W

AU - Durham, Stephen D.

PY - 2000/3

Y1 - 2000/3

N2 - 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.

AB - 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.

KW - Beta-binomial distribution

KW - Correlated binary data

KW - Developmental toxicology

KW - Extra-binomial variability

KW - Hierarchical model

KW - Intralitter correlation

KW - Litter effect

KW - Logistic regression

KW - Overdispersion

KW - Teratology

UR - http://www.scopus.com/inward/record.url?scp=0034063490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034063490&partnerID=8YFLogxK

M3 - Article

C2 - 10783786

AN - SCOPUS:0034063490

VL - 56

SP - 125

EP - 133

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 1

ER -