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I am curious about when it is recommended to use replicate weights in survey analysis. I compared the usual survey analysis with using replicate weights, as illustrated below.

Based on the paper "Resampling Variance Estimation for Complex Survey Data" The Stata Journal (2010), from what I understand (section 3.4), there seems to be no obvious preference between the two methods.

Any thoughts would be highly appreciated! Thanks!

library(survey)
data(api)

# stratified random sample
dstrat<-svydesign(id=~1,strata=~stype, weights=~pw, data=apistrat, fpc=~fpc)

svymean(~api00, dstrat)
svyby(~api00, by = ~stype, dstrat, svymean )

rstrat<-as.svrepdesign(dstrat)
svymean(~api00, rstrat)
svyby(~api00, by = ~stype, rstrat, svymean )

The results are exactly the same:

enter image description here

# cluster random sampling
dclus1<-svydesign(id=~dnum, weights=~pw, data=apiclus1, fpc=~fpc)
svyby(~api99, ~stype, dclus1, svymean)


redclus1<-as.svrepdesign(dclus1)
svyby(~api99, ~stype, redclus1, svymean)

The SEs seem to be quite different:

enter image description here

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It's preferable to use replicate weights when your data come with replicate weights rather than design metadata.

It's preferable to use replicate weights when you want to do an analysis that hasn't been implemented for linearisation.

Otherwise, there's no real preference. The standard error estimates will only be identical for linear functions (totals, stratum means) but they both estimate the same true standard error

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  • $\begingroup$ Dear Prof Lumley, thank you very much for your expertise! $\endgroup$ Oct 31, 2023 at 13:42

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