A nonparametric method to generate synthetic populations to adjust for complex sampling design features

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Qi Dong, Michael R. Elliott and Trivellore E. Raghunathan ^{Note 1}

Abstract

Outside of the survey sampling literature, samples are often assumed to be generated by a simple random sampling process that produces independent and identically distributed (IID) samples. Many statistical methods are developed largely in this IID world. Application of these methods to data from complex sample surveys without making allowance for the survey design features can lead to erroneous inferences. Hence, much time and effort have been devoted to develop the statistical methods to analyze complex survey data and account for the sample design. This issue is particularly important when generating synthetic populations using finite population Bayesian inference, as is often done in missing data or disclosure risk settings, or when combining data from multiple surveys. By extending previous work in finite population Bayesian bootstrap literature, we propose a method to generate synthetic populations from a posterior predictive distribution in a fashion 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 consider a simulation study with a stratified, clustered unequal-probability of selection sample design, and use the proposed nonparametric method to generate synthetic populations for the 2006 National Health Interview Survey (NHIS), and the Medical Expenditure Panel Survey (MEPS), which are stratified, clustered unequal-probability of selection sample designs.

Key Words

Synthetic populations; Posterior predictive distribution; Bayesian bootstrap; Inverse sampling.

Table of content

• 1. Introduction
• 2. Generating synthetic populations from survey data
• 3. Weighted finite population Bayesian bootstrap
• 4. Nonparametric method to generate synthetic populations
• 5. Inference from multiple nonparametric synthetic populations
• 6. Simulation studies
• 7. Application
• 8. Discussion
• Acknowledgements
• References

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Notes

1. Qi Dong, Netflix, Inc. 100 Winchester Cir, Los Gatos, CA 95032. E-mail: qidong@umich.edu; Michael R. Elliott, Department of Biostatistics, University of Michigan, 1420 Washington Heights, Ann Arbor, MI 48109, Survey Methodology Program, Institute for Social Research, University of Michigan, 426 Thompson St., Ann Arbor, MI 48106. E-mail: mrelliot@umich.edu; Trivellore E. Raghunathan, Department of Biostatistics, University of Michigan, 1420 Washington Heights, Ann Arbor, MI 48109, Survey Methodology Program, Institute for Social Research, University of Michigan, 426 Thompson St., Ann Arbor, MI 48106. E-mail: teraghu@umich.edu.