Generate correlation matrices with complex survey data in R

February 5, 2017
By

(This article was first published on R on Jacob Long, and kindly contributed to R-bloggers)

The survey package is one of R’s best tools for those working in the
social sciences. For many, it saves you from needing to use commercial
software for research that uses survey data. However, it lacks one
function that many academic researchers often need to report in
publications: correlations. The svycor function in jtools (more info) helps to
fill that gap.

An initial note, however, is necessary. The basic method behind this
feature comes from a response to a
question

about calculating correlations with the survey package written by
Thomas Lumley, the survey package author—he has not seen (to my knowledge) or endorsed this function. All that is good about this
function should be attributed to Dr. Lumley; all that is wrong with it
should be attributed to me (Jacob).

With that said, let’s look at an example. First, we need to get a
survey.design object. This one is built into the survey package.

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

Basic use

The necessary arguments are no different than when using svyvar.
Specify, using an equation, which variables (and from which design) to
include. It doesn’t matter which side of the equation the variables are
on.

svycor(~api00 + api99, design = dstrat)
    
##       api00 api99
## api00  1.00  0.98
## api99  0.98  1.00

You can specify with the digits = argument how many digits past the
decimal point should be printed.

svycor(~api00 + api99, design = dstrat, digits = 4)
##        api00  api99
## api00 1.0000 0.9759
## api99 0.9759 1.0000

Any other arguments that you would normally pass to svyvar will be
used as well, though in some cases it may not affect the output.

Statistical significance tests

One thing that survey won’t do for you is give you p values for the
null hypothesis that r = 0. While at first blush finding the p value
might seem like a simple procedure, complex surveys will almost
always violate the important distributional assumptions that go along with
simple hypothesis tests of the correlation coefficient. There is not a
clear consensus on the appropriate way to conduct hypothesis tests in
this context, due in part to the fact that most analyses of complex
surveys occurs in the context of multiple regression rather than simple bivariate cases.

If sig.stats = TRUE, then svycor will use the wtd.cor function
from the weights package to conduct hypothesis tests. The p values
are derived from a bootstrap procedure in which the weights define
sampling probability. The bootn = argument is given to wtd.cor to
define the number of simulations to run. This can significantly increase
the running time for large samples and/or large numbers of bootstraps.
The mean1 argument tells wtd.cor whether it should treat your sample size
as the number of observations in the survey design (the number of rows
in the data frame) or the sum of the weights. Usually, the former is
desired, so the default value of mean1 is TRUE.

svycor(~api00 + api99, design = dstrat, digits = 4, sig.stats = TRUE, bootn = 2000, mean1 = TRUE)
##       api00   api99  
## api00 1       0.9759*
## api99 0.9759* 1

When using sig.stats = TRUE, the correlation parameter estimates come
from the bootstrap procedure rather than the simpler method based
on the survey-weighted covariance matrix when sig.stats = FALSE.

By saving the output of the function, you can extract non-rounded
coefficients, p values, and standard errors.

c <- svycor(~api00 + api99, design = dstrat, digits = 4, sig.stats = TRUE, bootn = 2000, mean1 = TRUE)

c$cors
##           api00     api99
## api00 1.0000000 0.9759047
## api99 0.9759047 1.0000000
c$p.values
##       api00 api99
## api00     0     0
## api99     0     0
c$std.err
##             api00       api99
## api00 0.000000000 0.003467371
## api99 0.003467371 0.000000000

Technical details

The heavy lifting behind the scenes is done by svyvar, which from its
output you may not realize also calculates covariance.

svyvar(~api00 + api99, design = dstrat)
##       variance     SE
## api00    15191 1255.7
## api99    16518 1318.4

But if you save the svyvar object, you can see that there’s more than
meets the eye.

var <- svyvar(~api00 + api99, design = dstrat)
var <- as.matrix(var)
var
##          api00    api99
## api00 15190.59 15458.83
## api99 15458.83 16518.24
## attr(,"var")
##         api00   api00   api99   api99
## api00 1576883 1580654 1580654 1561998
## api00 1580654 1630856 1630856 1657352
## api99 1580654 1630856 1630856 1657352
## api99 1561998 1657352 1657352 1738266
## attr(,"statistic")
## [1] "variance"

Once we know that, it’s just a matter of using R’s cov2cor function
and cleaning up the output.

cor <- cov2cor(var)
cor
##           api00     api99
## api00 1.0000000 0.9759047
## api99 0.9759047 1.0000000
## attr(,"var")
##         api00   api00   api99   api99
## api00 1576883 1580654 1580654 1561998
## api00 1580654 1630856 1630856 1657352
## api99 1580654 1630856 1630856 1657352
## api99 1561998 1657352 1657352 1738266
## attr(,"statistic")
## [1] "variance"

Now to get rid of that covariance matrix…

cor <- cor[1:nrow(cor), 1:nrow(cor)]
cor
##           api00     api99
## api00 1.0000000 0.9759047
## api99 0.9759047 1.0000000

svycor has its own print method, so you won’t see so many digits past
the decimal point. You can extract the un-rounded matrix, however.

out <- svycor(~api99 + api00, design = dstrat)
out$cors
##           api99     api00
## api99 1.0000000 0.9759047
## api00 0.9759047 1.0000000

Suggestions welcome

Whether you see a problem with the method, found a bug, or have a suggestion for an enhancement, I’d like to hear it. Bug reports on Github are probably the best way to do that, but I’ll keep an eye out for comments here as well.

To leave a comment for the author, please follow the link and comment on their blog: R on Jacob Long.

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