Researchers are sometimes interested in converting a correlation matrix in to a covariance matrix. Perhaps they happen to use statistical software or an R package that can deal with covariance matrices as input, but not correlation matrices (e.g., the fantastic SEM package Lavaan (Rosseel, 2012), or the first step of the two-step meta-analytic SEM method implemented in the metaSEM package (Cheung, 2015). Or perhaps they are just inexplicably inquisitive and/or enjoy wasting hours performing pointless transformations.
Conveniently, the fantastic Lavaan has a built-in function for converting a correlation matrix in to a covariance matrix (others probably do too, but I don't know about them: forgive me). I'm going to show you how to use that function here because the Lavaan documentation does not show you how to use it in any real detail (as far as I can see).
First, you need to provide the correlation matrix. Simply duplicate the matrix that appears in the paper that you're interested in. For example, the one below from my friend Jennifer's paper on spitefulness and humor styles.
It needs to be symmetric, so you should fill upper and lower triangles of the matrix, in addition to a correlation of 1 for the variable with itself.
Use this code (it looks a lot better in the gist embedded below):
corr1 <- matrix(c( 1, -.47, -.16, -.18, -.26,
-.47, 1, .07, .04, .36,
-.16, .07, 1, -.13, -.10,
-.18, .04, -.13, 1, .19,
-.26, .36, -.10, .19, 1), nrow = 5, ncol = 5, byrow = FALSE)
The highlighted matrix and the code below should make it easier to identify from where the coefficients should be drawn and where they should go. Follow the colours.
Second, you need provide the standard deviations for each column (each variable, item, etc.).
Look at the SDs (above) and put them in the code below (in order!):
corr1sd = c(.65, .62, .68, .68, .66)
Third, you can perform the transformation using Lavaan's cor2cov function:
cov1 <- cor2cov(corr1, sds = corr1sd)
And there you have it. Covariances and variances on the diagonal. You can take this matrix forward in to a package that deals with it, such as metaSEM. Or you can play with it a bit and take in to Lavaan (blog to come on how to transform this matrix so it can be used in Lavaan or metaSEM).
Cheung, M. W. L. (2015). {metaSEM}: An R Package for Meta-Analysis using Structural Equation Modeling. Frontiers in Psychology. http://journal.frontiersin.org/article/10.3389/fpsyg.2014.01521/full
Yves Rosseel (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1-36. URL http://www.jstatsoft.org/v48/i02/
