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Abstract:
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An informative sampling design leads to unit inclusion probabilities that are correlated with the response variable of interest. However, multistage sampling designs may also induce higher order dependencies, which are typically ignored in the literature when establishing consistency of estimators for survey data. We relax the condition of asymptotic independence or asymptotic factorization and demonstrate that consistency is still achieved in the presence of residual sampling dependence. A popular approach for conducting inference on a population based on a survey sample is the use of a pseudo-posterior, which uses first order sampling weights to exponentiate the likelihood. We show that the pseudo-posterior is consistent not only for survey designs which have asymptotic factorization, but also for designs with unattenuated dependence. Using the National Survey on Drug Use and Health, we explore the impact of multistage designs and order based sampling. The use of the survey-weighted pseudo-posterior together with our relaxed requirements for the survey design establish a broad class of analysis models that can be applied to a wide variety of survey data sets.
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