# Calculate correlations and correlation tables with complex survey data

#### 2023-07-10

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 helps to fill that gap.

A note, however, is necessary. The initial motivation to add this feature comes from a response to a question about calculating correlations with the survey package written by Thomas Lumley, the survey package author. 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)

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

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

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 simulations. 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)

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$cors c$p.values