RE: Fixed elements within a block covariance matrix

From: GIRARD PASCAL - PASCAL.GIRARD@adm.univ-lyon1.fr Subject: RE: [NMusers] Fixed elements within a block covariance matrix Date: 1/13/2004 9:26 AM Hi Peter, Are you meaning you want initialize such a matrix in NONMEM ? If so you can try the following: 1) Renumber your Etas so that you will have the following structure: [X22 X32 X33 0 X31 X11] 2) This should be recognized by NONMEM as a band matrix (see attached (below) Diane Moulds Email for more explanations). 3) Tell us if that works! Cheers, Pascal Subject: Re: Termination due to rounding erros From: "diane r mould" Date: Fri, 23 Mar 2001 20:40:09 +0100 To: "KOWALSKI, KENNETH G. [PHR/1825]" , Dear Ken I will do the best I can :-) In NONMEM, a BAND matrix is when some of the elements in the off diagonal matrix have been set to zero. Doing this effectively fixes these elements to zero, eliminating the need for NONMEM to estimate those values which may not be identifiable, without sacrificing other identifiable elements. So if, for example, you have a one compartment model with CL, V, KA as parameters, if you can identify the covariance terms between CL and V and between CL and Ka, but not between Ka and V, a BAND matrix could be written to describe these relationships. Below is the NONMEM record for this, assuming that ETA(1) describes the variance on V, ETA(2) on CL and ETA(3) on KA. $OMEGA BLOCK(3) .1 .01 .1 0 .01 .1 No further coding is necessary. However, the elements in the BAND matrix must, of course, be symmetrical. Therefore a BAND matrix of $OMEGA BLOCK(3) .1 .01 .1 0 0 .1 will produce an error from NONMEM. You would need to code this arrangement instead as follows: $OMEGA BLOCK(2) .1 .01 .1 $OMEGA .1 I have found the use of the BAND matrix to be quite useful at times, particularly if the model is to be used later for simulation work for example. Best Regards Diane