Synthetic Multiple-Imputation Procedure for Multistage Complex Samples

Abstract

Multiple imputation (MI) is commonly used when item-level missing data are present. However, MI requires that survey design information be built into the imputation models. For multistage stratified clustered designs, this requires dummy variables to represent strata as well as primary sampling units (PSUs) nested within each stratum in the imputation model. Such a modeling strategy is not only operationally burdensome but also inferentially inefficient when there are many strata in the sample design. Complexity only increases when sampling weights need to be modeled. This article develops a general-purpose analytic strategy for population inference from complex sample designs with item-level missingness. In a simulation study, the proposed procedures demonstrate efficient estimation and good coverage properties. We also consider an application to accommodate missing body mass index (BMI) data in the analysis of BMI percentiles using National Health and Nutrition Examination Survey (NHANES) III data. We argue that the proposed methods offer an easy-to-implement solution to problems that are not well-handled by current MI techniques. Note that, while the proposed method borrows from the MI framework to develop its inferential methods, it is not designed as an alternative strategy to release multiply imputed datasets for complex sample design data, but rather as an analytic strategy in and of itself.

Keywords: Finite population Bayesian bootstrap; Haldane prior; clustered sample; sample weights; stratified sample.

Fig. 1

Correlation between variables in the simulated population (darker shades = higher correlation)

Fig. 2

Distribution of weights under the two subsampling schemes

Fig. 3

Comparison of methods for quantile estimation of BMI, by gender