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.