It depends on where those correlation matrices came from. For example,
suppose S1 is a sample covariance matrix of variables x1,..,xn (N1
observations) and S2 is a sample covariance matrix of other variables
z1,..,zm (N2 observations). Then (N1-1)S1 ~ W_n(V1, N1-1) and
(N2-1)S2~W_m(V2, N2-1) where W_p(V,k) is a pxp-dimenisonal Wishart
distribution with population covariance matrix V and k degrees of
freedom.
If N1 = N2, then one can think of an overall sample (m+n) x (m+n)
covariance matrix S formed form all m+n variables.In this case S1 is the
upper n x n diagonal block and S2 is the lower m x m diagonal block.
Expressions for the covariances between elements of S1 and elements of
S2 can be found in Chapter 7 of TW Andersen's book "An Introduction to
Multivariate Statistical Analysis" (Wiley).
If N1 ~= N2 then those expressions for the correaltions would have to be
modified.
On the other hand if all you have is two matrices without knowing where
they came from, you can't say anything about their correlation any more
than asking whether two numbers are "correlated".
Al Feiveson
-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
chichi@pob.huji.ac.il
Sent: Wednesday, May 09, 2007 10:44 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: correlation between two correlation matrices
I have two correlation matrices. How could I find the correlation
between them? In other words, how is one explained by the other?
----------------------------------------------------------------
This message was sent using IMP, the Internet Messaging Program.
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/