[R] Simulating from a Multivariate Normal Distribution Using a Correlation Matrix

Matthew David Sylvester msylvest at uclink.berkeley.edu
Fri Jun 25 09:48:51 CEST 2004

I would like to simulate randomly from a multivariate normal distribution using a correlation 
matrix, rho.  I do not have sigma.  I have searched the help archive and the R documentation as 
well as doing a standard google search.  What I have seen is that one can either use rmvnorm in 
the package: mvtnorm or mvrnorm in the package: MASS.  I believe I read somewhere that the latter 
was more robust.  I have seen conflicting (or at least seemingly conflicting to me, a relative 
statistics novice), views on whether one can use the correlation matrix with these commands 
instead of the covariance matrix.  I thought that if the commands standardized the covariance 
matrix, then it would not matter, but I end up with larger values when I test the covariance 
matrix versus when I test rho.  So, my question is, if one does not know sigma, can they use rho? 
 And, if so, which command (or is there another) is better to use?  I gather that both use eigen 
decomposition?  Thank you so much  in advance for your help.

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