Multiple imputation (MI) is a well-established method to handle item-nonresponse in sample surveys. Survey data obtained from complex sampling designs often involve features that include unequal probability of selection, clustering and stratification. Because sample design features are frequently related to survey outcomes of interest, the theory of MI requires including them in the imputation model to reduce the risks of model misspecification and hence to avoid biased inference. However, in practice multiply-imputed datasets from complex sample designs are typically imputed under simple random sampling assumptions and then analyzed using methods that account for the design features. Less commonly-used alternatives such as including case weights and/or dummy variables for strata and clusters as predictors typically require interaction terms for more complex estimators such as regression coefficients, and can be vulnerable to model misspecification and difficult to implement. We develop a simple two-step MI framework that accounts for complex sample designs using a weighted finite population Bayesian bootstrap (FPBB) method to generate draws from the posterior predictive distribution of the population. Imputations may then be performed assuming IID data. We propose different variations of the weighted FPBB for different sampling designs, and evaluate these methods using three studies. Simulation results show that the proposed methods have good frequentist properties and are robust to model misspecification compared to alternative approaches. We apply the proposed method to accommodate missing data in the Behavioral Risk Factor Surveillance System, the National Automotive Sampling System and the National Health and Nutrition Examination Survey III when estimating means, quantiles and a variety of model parameters.
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