Imputation under informative sampling

Imputed values in surveys are often generated under the assumption that the sampling mechanism is non-informative (or ignorable) and the study variable is missing at random (MAR). When the sampling design is informative, the assumption of MAR in the population does not necessarily imply MAR in the sample. In this case, the classical method of imputation using a model fitted to the sample data does not in general lead to unbiased estimation. To overcome this problem, we consider alternative approaches to imputation assuming MAR in the population. We compare the alternative imputation procedures through simulation and an application to estimation of mean erosion using data from the Conservation Effects Assessment Project.