In article <[EMAIL PROTECTED]>,
Rich Strauss <[EMAIL PROTECTED]> 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.
There are NO non-PSD (positive semi-definite) correlation
matrices. This follows from the square of a real number being
non-negative. I suggest you do a better job of investigating
the results of the postulated relationships; if the calculations
are correct, they can only produce PSD correlation matrices, and
if the variables are linearly independent, only PD correlation
matrices.
BTW, if your relationships are non-linear, the joint distribution
will NOT be normal. It seems to me that you need to consult with
people competent in probability and numerical analysis BEFORE you
use existing packages.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
