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"Certainty sampling units Stata's svy commands identify strata with an
FPC equal to one as units sampling with certainty. To properly
determine the design degrees of freedom, certainty sampling units
should be contained within their own strata, one for each certainty
unit, in each sampling stage. Although the observations contained in
certainty units have a role in parameter estimation, they contribute
nothing to the variance."

The last sentence isn't strictly true if sampling is without
replacement, but the later-stage contributions to standard errors are
usually very  small compared to those of the first-stage component,
because of the much higher numbers at the later stages.. Also, this
approach has the great advantage of giving sensible design degrees of
freedom, close to no. PSUs - no. Strata (after excluding the certainty

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