RE: Rounding errors
From: "KOWALSKI, KENNETH G. [PHR/1825]" <kenneth.g.kowalski@pharmacia.com>
Subject: RE: Rounding errors
Date: Fri, 23 Mar 2001 14:24:38 -0600
Diane,
See my comments and questions for clarification imbedded in your message in CAPS below.
Ken
Quoted reply history
-----Original Message-----
From: diane r mould [mailto:drmould@attglobal.net]
Sent: Friday, March 23, 2001 1:40 PM
To: KOWALSKI, KENNETH G. [PHR/1825]; nmusers@c255.ucsf.edu
Subject: Re: Termination due to rounding erros
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.
HOW DOES NONMEM KNOW THAT THE OFF-DIAGONAL ELEMENT IS TO BE FIXED TO ZERO? I THOUGHT YOU COULDN'T USE THE FIXED OPTION ON INDIVIDUAL ELEMENTS IN A BLOCK. DOESN'T NONMEM BALK AT THIS THINKING IT IS A PARAMETER WITH ZERO FOR A STARTING VALUE? I THOUGHT ALL ELEMENTS WITHIN A BLOCK MUST BE NON-ZERO.
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.
ACTUALLY THE ABOVE OMEGA BLOCK IS STILL SYMMETRICAL SO I'M NOT SURE WHY THIS EXAMPLE SHOULD BOMB BUT NOT THE FIRST EXAMPLE WITH ONLY ONE OFF-DIAGONAL SET TO ZERO.
You would need to code this arrangement
instead as follows:
$OMEGA BLOCK(2)
.1
.01 .1
$OMEGA .1
YES, THIS IS STANDARD BLOCKING OF AN OMEGA MATRIX (IE., ELEMENTS BETWEEN BLOCKS ARE UNCORRELATED BUT ELEMENTS WITHIN A BLOCK ARE CORRELATED).
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.
YES, IT IS IMPORTANT TO GIVE AS MUCH ATTENTION TO THE COVARIANCE STRUCTURE AS THE FIXED-EFFECTS STRUCTURAL MODEL IF YOU KNOW THE MODEL WILL BE USED FOR SIMULATION PURPOSES.