Re: permissible band matrix

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