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S Many applications use simple parametric models for the correlation structure of binary responses which are observed in clusters. The usual approach, to use correlation models appropriate for normally distributed responses, suffers from two drawbacks when the marginal probabilities within the clusters differ. First, as it does not explicitly take into account constraints on the second moments which must be satisfied for binary responses, it may fail to model realistically the range ofdoi:10.1093/biomet/88.1.287 fatcat:jkx35vjfyzgelakxfwkbxm35fu