### Abstract

Marginal models and conditional mixed-effects models are commonly used for clustered binary data. However, regression parameters and predictions in nonlinear mixed-effects models usually do not have a direct marginal interpretation, because the conditional functional form does not carry over to the margin. Because both marginal and conditional inferences are of interest, a unified approach is attractive. To this end, we investigate a parameterization of generalized linear mixed models with a structured random-intercept distribution that matches the conditional and marginal shapes. We model the marginal mean of response distribution and select the distribution of the random intercept to produce the match and also to model covariate-dependent random effects. We discuss the relation between this approach and some existing models and compare the approaches on two datasets.

Original language | English (US) |
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Pages (from-to) | 884-891 |

Number of pages | 8 |

Journal | Biometrics |

Volume | 60 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2004 |

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### Keywords

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

### ASJC Scopus subject areas

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