[R] Help : generating correlation matrix with a particular structure

Siew Leng TENG siewlengteng at yahoo.com
Sun Dec 12 12:15:24 CET 2004


I would like to generate a correlation matrix with a
particular structure. For example, a 3n x 3n matrix :
A_(nxn)   aI_(nxn)  bI_(nxn)
aI_(nxn)  A_(nxn)   cI_(nxn)
aI_(nxn)  cI_(nxn)  A_(nxn)

- A_(nxn) is a *specified* symmetric, positive
definite nxn matrix.
- I_(nxn) is an identity matrix of order n
- a, b, c are (any) real numbers

Many attempts have been unsuccessful because a
resulting matrix with any a, b, c may not be a
positive definite one, and hence cannot qualify as a
correlation matrix. Trying to first generate a
covariance matrix however, does not guarantee a
corresponding correlation matrix with the above

My larger purpose is to use this correlation matrix to
generate multivariate normal observations from the
corresponding covariance matrix (derived via cholesky
decomposition of the cor matrix).

Greatly appreciate any comments, if this is possible
or how this can be done.

Many grateful thanks and good day,

R-version used :
Windows version
Running on Windows XP

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