A friend's student asked for advice about a study in which I realized there's only one sampled unit per stratum. As none of the standard material on this apparent FAQ seemed to apply to what seemed a simple situation, I'm seeking advice about how to get a reasonable variance estimate.
The design: All counties in the U.S. (N = approx. 3000) were divided into three categories based on level of urbanization. For each of the 50 U.S. states, one county was drawn from each of the three categories, for a total sample of N = 150, i.e., 3 counties for each U.S. state. I'd conceptualize this as a sample with 150 strata, with strata defined by the 3 X 50 distinct combinations of State/Urbanzn. category, so that there is just one unit (county) sampled from each stratum. The probability of selection for each county is straightforward, i.e. 1/(number of counties of that size category in that state). County is the unit of analysis in the study.
I haven't used the -svy- features of Stata before, so I figured this was a nice example on which to educate myself, but then I realized I couldn't even compute the variance of an estimate of a mean, given that within-stratum variances estimates don't exist.
What might be a reasonable strategy here? All I can think is to recommend pweights but without -svy- estimators, and assume that that conventional variance estimators will overestimate the true variances, but that seems wrong.
The design: All counties in the U.S. (N = approx. 3000) were divided into three categories based on level of urbanization. For each of the 50 U.S. states, one county was drawn from each of the three categories, for a total sample of N = 150, i.e., 3 counties for each U.S. state. I'd conceptualize this as a sample with 150 strata, with strata defined by the 3 X 50 distinct combinations of State/Urbanzn. category, so that there is just one unit (county) sampled from each stratum. The probability of selection for each county is straightforward, i.e. 1/(number of counties of that size category in that state). County is the unit of analysis in the study.
I haven't used the -svy- features of Stata before, so I figured this was a nice example on which to educate myself, but then I realized I couldn't even compute the variance of an estimate of a mean, given that within-stratum variances estimates don't exist.
What might be a reasonable strategy here? All I can think is to recommend pweights but without -svy- estimators, and assume that that conventional variance estimators will overestimate the true variances, but that seems wrong.
