Handling survey nonresponse in cluster sampling

In surveys under cluster sampling, nonresponse on a variable is often dependent on a cluster level random effect and, hence, is nonignorable. Estimators of the population mean obtained by mean imputation or reweighting under the ignorable nonresponse assumption are then biased. We propose an unbiased estimator of the population mean by imputing or reweighting within each sampled cluster or a group of sampled clusters sharing some common feature. Some simulation results are presented to study the performance of the proposed estimator.