Accommodating survey weights in multiple imputation Seminar

Abstract
Multiple imputation (MI) is a principled method to deal with item-level missing data that has become increasingly popular in the public health and social science investigations where data production is often based on complex sample surveys. However, existing software packages and procedures typically do not incorporate complex sample design features in the imputation process. Failure to account for design features, particularly sampling weights, can introduce bias on final estimates. Recent work to accommodate complex sample designs in imputation includes the sample design in the formulation of the imputation model, which typically requires strong model assumptions and can involve expensive computation in practice. We propose a new method to incorporate complex sample designs in MI, using recent work (Dong 2012) that extends finite population Bayesian bootstrap to generate synthetic populations from a posterior predictive distribution in a fashion that inverts the complex sampling design features and generates simple random samples from a superpopulation point of view, making adjustment on the complex data so that they can be analyzed as simple random samples. We then perform conventional parametric MI for missing data at the second step using readily available imputation software designed for an SRS sample. A new combining rule for the point and variance estimates is derived to make valid inferences based on the two-step procedure. We evaluate the performance of the new method in comparison with the fully model-based method through a simulationdesign. Results show that the new method is more robust to model misspecification and generally yields lower RMSE than the fully model-based method.