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Marginalized Binary Mixed‐Effects Models with Covariate‐Dependent Random Effects and Likelihood Inference
Author(s) -
Wang Zengri,
Louis Thomas A.
Publication year - 2004
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2004.00243.x
Subject(s) - covariate , marginal model , random effects model , marginal distribution , mathematics , conditional probability distribution , inference , statistics , econometrics , marginal likelihood , generalized linear mixed model , quasi likelihood , regression analysis , computer science , random variable , count data , maximum likelihood , artificial intelligence , poisson distribution , medicine , meta analysis
Summary 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.