Estimation of a cluster-level regression model under nonresponse within clusters

When sample surveys are clustered and subject to non-response, it is possible to study cluster-level association between response rates and cluster-level quantities derived from survey variables. The existence of association may suggest informative nonresponse with possible biasing effects. In this paper, this problem is studied for the case where the aim is to fit a cluster-level regression model. Two possible underlying models for nonresponse with potential biasing effects are considered. Alternative estimators of regression coefficients under these models are proposed. The properties of these estimators are studied in two simulation studies and with real data from a survey of employees, where the clusters consist of workplaces.