How to generate a variable with with fixed correlations to an existing variable which already has a uniform distribution

[Sebastian Munoz]

Hi, I have generate a variable which I have called X, it has a uniform distribution like this: gen x=runiform(0,2). I want to create another variable, called it Y, that has a fixed correlation with X. For instance 0.5. I have already tried commands such as corr2data but they do not work the way I want to. I will sincerely appreciate a little help with my problem, thank you very much.

[William Lisowski]

Welcome to Statalist.

You've not told us what distribution you want the variable Y to have. If it too is intended to be uniform, then Dimitriy V. Masterov has answered that question in a different forum at

https://stackoverflow.com/questions/...m0-1-variables

[Dimitriy V. Masterov]

The general procedure I outlined on SO should also work for the non-uniform case, though you will have to use the appropriate inverse CDF for the third step.

Here's in example where Y~N[100,15^2]:

clear

// Step 1
matrix C = (1, .512 \ .512, 1) // useful to bump the correlation up from what you desire
corr2data x y, n(10000) corr(C)

// Steps 2-3
replace x = normal(x) // step 3 not needed for uniform [0,1]
replace y = 100 + 15*invnormal(normal(y))

// Check that everything looks OK
hist x, addplot(function y=1, range(0 1))
hist y, normal
corr x y, means