Pearson correlation coefficient in R's survey package

Question

Sorry if this is really obvious, but I can't see how to do a simple Pearson correlation between two variables in the survey package. My data has strata so it would be the equivalent to finding r for api00 and api99 in apistrat.

library(survey)
data(api)

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

I'm sure there must be a simple way of doing it using svyvar or svyglm or something but I can't see it?

Answer 1

You can use svyvar to estimate the variance-covariance matrix, and then scale it to the correlation:

library(survey)
data(api)

dstrat <- svydesign(id=~1,strata=~stype, weights=~pw, data=apistrat, fpc=~fpc)
v <- svyvar(~api00+api99, dstrat)

as.matrix(v)
cov2cor(as.matrix(v))

This works for any number of correlations and any design.

Answer 2

library(survey)
data(api)
dstrat<-svydesign(id=~1,strata=~stype, weights=~pw, data=apistrat, fpc=~fpc)
summary(svyglm(api00~ell+meals+mobility, design=dstrat),correlation=T)

Answer 3

I've been thinking around the problem a bit and I'm starting to think the best way forward might be to just scale both of the variables first, presumably using svymean and svyvar.

dstrat2 <- transform(dstrat, 
                     z_api99 = (api99 - svymean(~api99,    dstrat))/sqrt(svyvar(~api99, dstrat)), 
                     z_api00 = (api00 - svymean(~api00, dstrat))/sqrt(svyvar(~api00, dstrat))) 

svyglm(z_api99 ~ z_api00, dstrat2)$coefficients

This gives 9.759047e-01, which is the same result as using:

library(weights)
wtd.cor(apistrat$api99, apistrat$api00, weight = apistrat$pw)

It has the advantage that it could be used with pretty much any survey design type. It also provides a way of getting the standardised beta coefficients if there are more variables. It isn't quite what I was after with the original question, but it might be the best way if there isn't a specific option.

If anyone else can confirm if this works or not, or if there is a better way, then I'd be very grateful for any further comments.