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Marginalized Binary Mixed-Effects Models with Covariate-Dependent Random Effects and Likelihood Inference

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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.

Keywords: Bridge distribution; Clustered data; Gaussian–Hermite quadrature; Marginal model; Random-effects model

Document Type: Research Article


Affiliations: 1: Medtronic Inc., Saint Paul, Minnesota 55126, U.S.A., Email: 2: Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland 21205, U.S.A., Email:

Publication date: December 1, 2004


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