1. Introduction
Qi Dong, Michael R. Elliott and Trivellore E. Raghunathan
Survey agencies often repeatedly draw samples from similar populations and collect similar variables, sometimes even using the same frame. For example, the National Health Interview Survey (NHIS) and the National Health and Nutrition Examination Survey (NHANES) are both conducted by the U.S. National Center for Health Statistics. These two surveys target the U.S. non-institutionalized population and have a considerable overlap of questions. By combining information from multiple surveys, we hope to obtain more accurate inference for the population than if we use the data from a single survey.
One of the biggest challenges in such combining is the compatibility of multiple data sources. Surveys may use different sampling designs or modes of data collection, which may result in various sampling and nonsampling error properties. Instead of directly pooling the data from multiple surveys for a simple analysis, we need to adjust for the discrepancies among the data to make them comparable.
Various methods for combining data collected in two surveys have been proposed in the survey methodology literature (Hartley 1974; Skinner and Rao 1996; Lohr and Rao 2000; Elliott and Davis 2005; Raghunathan, Xie, Schenker, Parsons, Davis, Dodd and Feuer 2007; Schenker, Gentleman, Rose, Hing and Shimizu 2002; Schenker and Raghunathan 2007; Schenker, Raghunathan and Bondarenko 2009). The most recent papers by Raghunathan et al. (2007) and Schenker et al. (2009) applied model-based approaches. The basic idea for the model-based approach is to fit an imputation model to the data of better quality and use the fitted model to impute the values in the other samples of lower quality. As long as the imputation model is correctly specified, this approach can take advantage of the strengths of the multiple data sources and improve the statistical inference. However, as suggested by Reiter, Raghunathan and Kinney (2006), when the sample is collected using complex sampling designs, ignoring those features could result in biased estimates from the design-based perspective. However, fully accounting for the complex sampling design features in practice is very difficult. For example, both Raghunathan et al. (2007) and Schenker et al. (2009) used a simplified method to adjust for stratification and clustering. Raghunathan et al. (2007) used a rudimentary concept of design effect and Schenker et al. (2009) used propensity scores to create adjustment subgroups for modeling.
Here we propose a new method for combining multiple surveys that adjusts for the complex sampling design features in each survey. The unobserved population in each survey will be treated as missing data to be multiply imputed. The imputation model will account for complex design features using a recently developed nonparametric synthetic population generation method (Dong, Elliott and Raghunathan 2014). For each survey, the observed data and the multiply imputed unobserved population produce multiple synthetic populations. Once the whole population is generated, the complex sampling design features such as stratification, clustering and weighting will be of no use in the analysis and the synthetic populations can be treated as equivalent simple random samples. Finally, the estimate for the population quantity of interest will be calculated from each synthetic population and then will be combined first within each individual survey and then across multiple surveys.
This paper proceeds as follows: Section 2 summarizes generating synthetic population while accounting for complex sampling design features using the nonparametric approach. Section 3 describes methodology to produce combined estimates from these multiple synthetic populations. In Section 4, we apply the proposed method to combine the 2006 NHIS and the Medical Expenditure Panel Survey (MEPS) to estimate the health insurance coverage rates of the US population. Section 5 concludes with discussion and directions for future research.
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