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Going through the a course on Survey Weights and it says that even though a dataset may sample using 3 clusters (like Counties, City Blocks, and households), you only need to specify the first level of clustering when using svydesign() for weighting.

Why is that? Shouldn't you specify every level of clustering if you are trying to weight correctly? Because the sampling was done with 3 levels of clustering?

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the clustering is a correction for simple random sampling.. not sure exactly what you're looking at, but if the second and third levels are simple random samples within the first (non-SRS) then it might make mathematical sense to only specify the first in the survey design. in other words, counties might be non randomly chosen to assure sufficient urban rural mix, though within each county, city blocks and then households can be randomly sampled and thus not need a sampling correction?

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You ideally should specify all the stages, but there's a common approximation of specifying the full weights but only strata and clusters at the first stage, and then pretending the clusters were sampled with replacement. This 'with-replacement' approximation is surprisingly accurate when all the sampling probabilities for individuals are either 100% or fairly small, which tends to be the case in national surveys.

The reason for using the approximation is twofold

  • Specifying the full sampling design can be problematic for confidentiality reasons
  • Code to handle the full sampling design is more complicated. In the past, it might have been hard to find software that did it correctly.

Public-use datasets from large national surveys are often only published with stage-one information, so external users have to use the approximation.

There are some national survey datasets where the approximation isn't good. For example, Stats Canada have some post-census follow-up surveys of First Nations people with high sampling rates in some communities. And non-national surveys might well have high sampling fractions in some groups and need more detailed variance calculations

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