On Tue, 16 Nov 1999, Rich Strauss wrote:
> I have a problem that I had initially thought would be straightforward (but
> then, what is?). For a Monte Carlo-type simulation study, I want to be
> able to to generate sets of pseudorandom numbers having correlations equal
> to (or differing only randomly from) a target correlation matrix that I
> specify up front, based on postulated relationships among variables. This
> is very easy to do using the classic method of Kaiser & Dickman (1962), as
> long as the target correlation matrix is positive definite (PD) (ie, has
> all positive eigenvalues). If not, the algorithm (programmed in Matlab)
> returns complex numbers, which are not satisfactory for my purposes.
>
A correlation matrix must be symmetric and positive semi-definite
(non-negative eigenvalues). Are your eigenvalues negative or just 0?
If some are negative, there is a specification error. If none are
negative but some are zero, some variables are linear combinations of
others. These can be omitted from the random number generation.
___________________________________________________________________________
Michael P. Cohen phone 202-219-1917
National Center for Education Statistics fax 202-219-1736
555 New Jersey Avenue NW #402 Internet [EMAIL PROTECTED]
Washington DC 20208-5654 USA
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