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Abstract:
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Estimates of direct survey variances for areas with small sample sizes is problematic especially when combined with complex survey designs. However, reasonable estimates of these variances (or their associated design effects / effective sample sizes) are important when modeling data from these surveys. One important application is area-level small area models such as Fay and Herriot (1979). Other model-based uses include calibrating the likelihood to reflect the amount of uncertainty relative to a simple random sample. An ad hoc practice to estimate design effects or effective sample size for counts and rates in small areas and domains is to estimate the design effect for a larger aggregate and assume that the component areas or domains have the same design effect. This is valid only under restrictive conditions. Starting from the framework of a stratified sample, we will explore how the design effect at the aggregated level compares to the design effects at the lower level. We will study these design effects and propose a method to estimate them under several scenarios: unequal probability selection, unequal area means, and clustering within area.
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