[R] How to generate regression matrix with correlation matrix
Spencer Graves
spencer.graves at pdf.com
Fri Jul 11 23:53:50 CEST 2003
What problem are you really trying to solve? The problem statement
as I read it contains two logical contradictions that I see:
1. Orthonormal means X'X = Identity matrix (10 x 10). That means
the pairwise correlation coefficients can NOT be different from 0.
2. Not all symmetric matrices with 1's on the diagonal and random
numbers U(-1, 1) on the off diagonal are correlation matrices. Consider
the following example:
Cormat <- array(c(1, -0.9, -0.9, -0.9, 1, -0.9, -0.9, -0.9, 1),
dim=c(3,3))
> Cormat
[,1] [,2] [,3]
[1,] 1.0 -0.9 -0.9
[2,] -0.9 1.0 -0.9
[3,] -0.9 -0.9 1.0
> eigen(Cormat)
$values
[1] 1.9 1.9 -0.8
The fact that one eigenvalue is negative means that this "Cormat" is not
positive definite.
hope this helps. spencer graves
rui wrote:
> Dear R community:
>
> I want to simulate a regression matrix which
is generated from an orthonormal matrix X of
dimension 30*10 with different between-column
pairwise correlation coefficients generated from
uniform distribution U(-1,1).
>
> Thanks in advance!
>
> Rui
> [[alternative HTML version deleted]]
>
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