Date:         Tue, 6 May 2008 15:44:14 -0400
Reply-To:     Cordelia Flynn <prime431@YAHOO.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Cordelia Flynn <prime431@YAHOO.COM>
Subject:      Simulating variance components + Cholesky

When simulating a data vector, why do we use
the square roots of the variance components ?

For example, to simulate both variance
components of a simple mixed effects model,
suppose the between-subject variance is 3,
while the within-subject variance is 10. So
assuming  b ~ n(0,sig2B), e ~ n(0,sig2), the
data vector has form,

         y = mu + beta + a + e.

Then sample code to generate, say, 100 records
of 2-level treatment data can have form:

data a;
do sim=1 to 100;
  do beta=1 to 2;
  a=rannor(0)*sqrt(3);
   do n=1 to 5;
   e=rannor(0)*sqrt(10);
   y = 100 + beta + a + e;
   output;
   end;
  end;
end;

So why have the square root of the var comps
instead of the whole term ?

Also, what role does the Cholesky decomposition
play in data simulation? Any references ?

Thanks Friends,

Cordelia Flynn
Lancaster, PA