  Multiple imputation provides an effective way to handle missing data. When
several possible models are under consideration for the data, the multiple
imputation is typically performed under a single-best model selected from the
candidate models. This single model selection approach ignores the uncertainty
associated with the model selection and so leads to underestimation of the
variance of multiple imputation estimator. In this paper, we propose a new
multiple imputation procedure incorporating model uncertainty in the final
inference. The proposed method incorporates possible candidate models for the
data into the imputation procedure using the idea of Bayesian Model Averaging
(BMA). The proposed method is directly applicable to handling item nonresponse
in survey sampling. Asymptotic properties of the proposed method are
investigated. A limited simulation study confirms that our model averaging
approach provides better estimation performance than the single model selection
approach.
