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:
do sim=1 to 100;
do beta=1 to 2;
do n=1 to 5;
y = 100 + beta + a + e;
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 ?