Thanks everyone for your kindly reply. I have Al's reply posted below. The
explanation and S+ codes provided by Al Maloney is helpful.
Sam
======================================
Hi Sam,
I expect you will get better replies, but here is a short answer. The
proposed matrix is not positive definite (i.e. you have at least 1 negative
eigenvalue). Said in a nicer way, your var-cov matrix must be consistent
with itself. That is, you can't have a very strong correlation between
parameters 1 and 2 (say 0.99), and between 1 and 3 (say 0.99), but then have
no correlation between 2 and 3 (in this case, the strongest correlation you
can have is 1/sqrt(2) I think (about 0.7).
To solve your problem, you will either need to reduce some correlations that
are non-zero, or increase some correlations that are currently zero.
Here are a few lines of SPLUS code that will give the eigenvalues. The first
gives a negative eigenvalue, but the second has all postive eigenvalues, and
hence should work in NONMEM.
doesnotwork=t(cbind(c(0.09,0.07,0,0),c(0.07,0.09,0.07,0),c(0.0,0.07,0.09,0.0
7), c(0.0,0.0,0.07,0.09)))
neweigen = eigen(doesnotwork, symmetric = TRUE)
neweigen$values
doeswork=t(cbind(c(0.09,0.05,0,0),c(0.05,0.09,0.05,0),c(0.0,0.05,0.09,0.05),
c(0.0,0.0,0.05,0.09)))
neweigen2 = eigen(doeswork, symmetric = TRUE)
neweigen2$values
good luck,
AL
OMEGA matrix should be positive definite, and the one that you use is
not of this class:
> b <- 7
> a <- 9
> b1 <- 7
> aa <- matrix(c(a,b1,0,0,b1,a,b,0,0,b,a,b1,0,0,b1,a),4,4)
> aa
[,1] [,2] [,3] [,4]
[1,] 9 7 0 0
[2,] 7 9 7 0
[3,] 0 7 9 7
[4,] 0 0 7 9
> det(aa)
[1] -2945
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Sam Liao wrote:
Dear NONMEM users:
Can someone please help me to solve this problem with a band matrix?
$OMEGA BLOCK(4)
0.09 ;BSV_V1C
0.07 0.09 ;BSV_CLC
0 0.07 0.09 ;BSV_CLN
0 0 0.07 0.09 ;BSV_V1N
Why this one above is getting an error in NONMEM?
$OMEGA BLOCK(4)
0.09 ;BSV_V1C
0.07 0.09 ;BSV_CLC
0 0 0.09 ;BSV_CLN
0 0 0.07 0.09 ;BSV_V1N
This one above is fine, but I need to run a simulation in which there
are some correlation between CLC and CLN.
There were some very helpful discussion on band matrix few years
ago. But I still couldn't figure out why this band matrix not
permissible.
Sam Liao
<http://www.cognigencorp.com/nonmem/nm/96mar232001.html>
