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I'm currently working with data related to education that was collected in different geographic regions. Included with the data are weights and strata, meaning Stata svyset is needed. However, when I use it, I get an error related to "Missing standard error because of stratum with single sampling unit."

According to the documentation from Stata (here) there are three different ways of dealing with this:

The first one, singleunit(certainty), will treat strata with singleton PSUs as certainty units, so those strata contribute nothing to the standard error. The second option, singleunit(scaled), is a scaled version of singleunit(certainty). The scaling factor comes from using the average of the variances from the strata with multiple sampling units for each stratum with a singleton PSU. The third option, singleunit(centered), specifies that strata with singleton PSUs be centered at the grand mean instead of the stratum mean.

I do not understand how to pick between these techniques. I've looked at this and can confirm the standard errors are different depending on which technique is selected. Given the data was collected with the intent of all strata being used, the first option (certainty) seems inappropriate. Although all data are represented (I did not exclude observations, only create a sub-population for analysis) either scaled or centered seem viable. Which option is statistically justifiable and how does one pick?

When searching for help with this there is much about 'how it works' rather than why one method is appropriate for given circumstances. My question is not about the underlying code, only about what scenarios each technique would be most appropriate to use or how to tell the difference between when to use each technique.

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  1. You should use certainty if the singleton PSUs were sampled with certainty and you aren't using the 'with replacement' approximation to the design. Otherwise, don't. If this is the case, you will likely know.

If the sampling isn't with certainty there is no unbiased estimator of the variance, so nothing is exactly right, and both the other options are reasonable. Ideally, the people who designed the survey will know why they had a singleton PSU and will tell you what they think you should do. If not:

  1. The centered option is conservative, which is a good argument for using it, since survey standard errors seem to be underestimated pretty often.

  2. One rationale for the scaled approach is when you get singleton PSUs because of missing data in a design with many two-PSU strata. It seems reasonable in that setting to treat those strata as approximately representative and scale up the variance from the other strata pro rata

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