5. Discussion
Qi Dong, Michael R. Elliott and Trivellore E. Raghunathan
In this paper, we propose a new method to combine information from multiple complex surveys. We apply the new method to combine information about health insurance status from the 2006 NHIS, MEPS, and BRFSS. Results show that the combined estimate is more precise compared to the estimates from individual surveys. As previous work has shown (Dong et al. 2014), we have little information loss in the sense that the sampling properties of inferences from the synthetic population and the actual sample are very similar. Thus when we combine the estimates from three samples, the combined estimate is substantially more efficient that the estimates from individual surveys. (We note that this application is primarily for illustrative purposes; similar inferences could be made by computing the design-based estimates and variances for each of the surveys, then applying the combining rule in (3.2) on the design-based estimates.)
This new combining survey method has two major advantages over the existing methods. First, the approach used here to generate synthetic populations, discussed in detail in Dong et al. (2014), accounts for the complex sample design nonparametrically using extensions of finite population Bayesian bootstrap methods. Since the resulting synthetic populations can be analyzed as simple random samples, information from other surveys can be used to adjust for the nonsampling errors and/or filling in the missing variables. Another advantage of this method is it has no limitation on the number of surveys to be combined as long as the surveys have the same underlying population. The proposed method that adjusts for the complex sampling design features can be applied to each survey independently. After the missing information is imputed, regardless the number of surveys to be combined, we only need to combine the estimates from each survey using the combing rule developed in this manuscript. A final advantage of the proposed approach is the ability of the synthetic populations generated by the nonparametric method to preserve the item-missing values in the actual data. This potentially fills in a gap in the multiple imputation area that existing imputation methods typically ignore the complex sampling design features in the data and impute the missing values as if they are simple random samples. We consider this application in future work.
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