The relationship between marginal (population-averaged) models for cluster-correlated binary data, and a class of cluster-specific, logistic-normal random effects models is discussed. We show that random effects models can accomplish the same end as a more direct modelling of intra-cluster correlation, as in GEE.

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Keywords Cluster-specific models, Clustered data, Correlated binary responses, Population-averaged models, Random effects models
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Journal Statistics and Probability Letters
Sashegyi, A.I. (Andreas I.), Brown, K.S. (K. Stephen), & Farrell, P. (2001). On the correspondence between population-averaged models and a class of cluster-specific models for correlated binary data. Statistics and Probability Letters, 52(2), 135–144. doi:10.1016/S0167-7152(00)00183-8