How does the R survey package svydesign() function adjust for clustering?

Question

R survey package svydesign() function adjust for clustering? If I input PSU and school [svydesign(ids=~PSUID+school, weights=~w, data=data1)] how does it work?

Can't find the information anywhere

Answer 1

There isn't a simple answer to this: it's not just a closed-form expression, it's a recursive computation. It's documented with references in ?svyrecvar

What it computes, though, is the Horvitz-Thompson variance estimator, eg here