### Abstract

Random effects logistic regression models are often used to model clustered binary response data. Regression parameters in these models have a conditional, subject-specific interpretation in that they quantify regression effects for each cluster. Very often, the logistic functional shape conditional on the random effects does not carry over to the marginal scale. Thus, parameters in these models usually do not have an explicit marginal, population-averaged interpretation. We study a bridge distribution function for the random effect in the random intercept logistic regression model. Under this distributional assumption, the marginal functional shape is still of logistic form, and thus regression parameters have an explicit marginal interpretation. The main advantage of this approach is that likelihood inference can be obtained for either marginal or conditional regression inference within a single model framework. The generality of the results and some properties of the bridge distribution functions are discussed. An example is used for illustration.

Original language | English (US) |
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Pages (from-to) | 765-775 |

Number of pages | 11 |

Journal | Biometrika |

Volume | 90 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2003 |

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### Keywords

- Bridge distribution function
- Clustered data
- Gaussian-Hermite quadrature
- Marginal model
- Random effects model

### ASJC Scopus subject areas

- Statistics and Probability
- Mathematics(all)
- Agricultural and Biological Sciences (miscellaneous)
- Agricultural and Biological Sciences(all)
- Statistics, Probability and Uncertainty
- Applied Mathematics