A model is proposed for the binary data analog of the paired t situation. In this model the success probabilities vary across strata and have a specified probability distribution. The parameters can be estimated by moments or likelihood methods; various large-sample tests are proposed. The estimates and tests do not require fixed sample sizes. The model can be applied to case-control studies in which at least some cases have multiple controls and to other nested designs that have two treatments per stratum and small samples in each treatment-stratum combination.
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Mary Patricia Coffey (1988) studied this question.
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