Specifying a Correlation

[Jared Greathouse]

Say I'd like to simulate academic data

clear *

set seed 1066
cls

matrix input mCorr = (1, .3, .4\  .3, 1, 0, \  .4, 1, 1)
corr2data gpa gre final, n(2500)  means(3.5 150 80) sds(.15 4 2) corr(mCorr)

corr

I want there to be a correlation between GRE test scores (GRE) ones gpa, and their final grade, with GRE being between 130 and 165 and GPA being between 2 and 4.5, and final being between 0 and 100. How might I specify, say, a correlation between these three variables? I know it has something to do with this matrix command above... at present, Stata returns

. corr2data gpa gre final, n(2500)  means(3.5 150 80) sds(.15 4 2) corr(mCorr)
corr(mCorr) is not symmetric

How might I solve this? I've always wondered how we can perfectly (almost) specify a relationship between a set of variables, since this would come in handy in a simulation setting. I figured the easiest setting would be to use an academic example where the variables are pretty sensible to consider (i.e., better tests = better grades).

[Clyde Schechter]

You made an error in specifying the contents of matrix mCorr. A correlation matrix must be symmetric. But you have mCorr[2,3] = 0 and mCorr[3,2] = 1.

Personally, I doubt that either 0 or 1 is a realistic estimate of the correlation between gre and final (whatever final is), but in any case you have to pick something and use it consistently.

For example:

. matrix input mCorr = (1, .3, .4\  .3, 1, 0 \  .4, 0, 1)

.
. corr2data gpa gre final, n(2500)  means(3.5 150 80) sds(.15 4 2) corr(mCorr)
(obs 2,500)

.
. corr gpa gre final
(obs=2,500)

             |      gpa      gre    final
-------------+---------------------------
         gpa |   1.0000
         gre |   0.3000   1.0000
       final |   0.4000   0.0000   1.0000