The SPSS syntax below generates random variables with a specified
correlation matrix. I didn't write it, I believe I found it on an
discussion list (perhaps this one?). I have used it and it seems to work
well. I don't recall the details of how it all works, but I do remember
that if you ponder it for a while it is not hard to modify to different
purposes.
Good Luck
Brad
input program.
+ loop #i = 1 to 10000.
+ do repeat response=r1 to r5 .
+ compute response = normal(1) .
+ end repeat.
+ end case.
+ end loop.
+ end file.
end input program.
correlations r1 to r5 / statistics=descriptives.
* Factor procedure computes pr1 to pr5, which are standard MVN .
factor variables = r1 to r5 / print = default det
/criteria = factors(5) /save=reg (all,pr).
* use matrix to set corr matrix.
* x is a 10,000 by 5 matrix of independent standard normals .
* cor is the target covariance matrix.
* cho is the Cholesky factor of cor .
* newx is the 10,000 by 5 data matrix which has target covariance matrix .
matrix.
get x / variables=pr1 to pr5.
compute cor={1, 0.4, 0.3, 0.2, 0.1 ;
0.4, 1, 0.4, 0.3, 0.2 ;
0.3, 0.4, 1, 0.4, 0.3 ;
0.2, 0.3, 0.4, 1, 0.4 ;
0.1, 0.2, 0.3, 0.4, 1 }.
compute deter=det(cor).
print deter / title "determinant of corr matrix" / format=f10.7 .
print sval(cor) / title "singular value decomposition of corr".
print eval(cor) / title "eigenvalues of input corr".
* In a symmetric matrix sval and eigenvalues are identical - choose 1 .
compute condnum=mmax(sval(cor))/mmin(sval(cor)).
print condnum / title "condition number of corr matrix" / format=f10.2 .
compute cho=chol(cor).
print cho / title "cholesky factor of corr matrix" .
compute chochek=t(cho)*cho.
print chochek / title "chol factor premult by its transpose " /format=f10.2
.
compute newx=x*cho.
compute newx=newx*15 + 100.
save newx /outfile=* /variables= nr1 to nr5.
end matrix.
correlations nr1 to nr5 / statistics=descriptives.
