Correlated nonresponse within clusters arises in certain survey settings. It is often represented by a random effects model and assumed to be cluster-specific nonignorable, in the sense that survey and nonresponse outcomes are conditionally independent given cluster-level random effects. Two basic forms of inverse probability weights are considered: response propensity weights based on a marginal model, and weights based on predicted random effects. It is shown that both approaches can lead to biased estimation under cluster-specific nonignorable nonresponse, when the cluster sample sizes are small. We propose a new form of weighted estimator based upon conditional logistic regression, which can avoid this bias. An associated estimator of variance and an extension to observational studies with clustered treatment assignment are also described. Properties of the alternative estimators are illustrated in a small simulation study
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