RE: $OMEGA blocks and log-likelihood profiling
From: Leonid Gibiansky lgibiansky@emmes.com
Subject: RE:[NMusers] $OMEGA blocks and log-likelihood profiling
Date: Tue, June 1, 2004 10:43 am
Justin
I'll leave the bootstrap/LLP comparison to others, but if you really want
to do LLP for OMEGA, you need to express those in terms of THETA
parameters. For diagonal OMEGA matrix it is trivial:
$PK
CL=THETA(1)*EXP(SQRT(THETA(11))*ETA(1))
V=THETA(2)*EXP(SQRT(THETA(22))*ETA(2))
.....
$OMEGA
1 FIXED
1 FIXED
Here you can LLP THETA(11) and THETA(22) that are equivalent to OMEGA11,
OMEGA22
For off-diagonal elements it is more tricky. One possibility is to express
the model in terms of
META1=THETA()*ETA(1)
META2=THETA()*ETA(1)+THETA()*ETA(2)
META3=THETA()*ETA(1)+THETA()*ETA(2)+THETA()*ETA(3)
......
CL=THETA()*EXP(META1)
etc.
and profile those THETA-coefficients (this is also the way to check for
significance of each of the off-diagonal elements/correlations via
LL). OMEGA elements are easily expressed in terms of THETAs.
Leonid