RE: Rounding errors
From: "KOWALSKI, KENNETH G. [PHR/1825]" <kenneth.g.kowalski@pharmacia.com>
Subject: RE: Rounding errors
Date: Fri, 23 Mar 2001 16:32:48 -0600
Diane, Bill, ALL
Thanks. OK now I understand.
In Diane's examples,
> $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
both of the omega blocks represent symmetrical matrices but only the first example is BAND-symmetric. Band symmetric implies that all elements on a diagonal must be the same. I'm not sure how valuable this is. How often are we in a situation say where we want to assume that the variances for ka, V and CL are the same and that the covariance between ka and V is the same as the covariance between V and CL?
Band-symmetric matrices may indeed reduce the dimensionality of omega so as to get rid of the overparameterization problem but I really wonder how often such matrices lead to the most parsimonious form for omega? I could envision cases where a full unstructured matrix may be overparameterized and fitting a diagonal omega converges and leads to a lower objective function than a band-symmetric matrix. Perhaps because the diagonal omega allows for different values on the diagonal that the band-symmetric matrix does not. Even if the full unstructured matrix is giving some indication that certain etas should be correlated, forcing the variances to be the same using the band-symmetric form may be worse (increase in ELS) relative to forcing all the covariances to be zero in a diagonal matrix.
Ken
Quoted reply history
-----Original Message-----
From: Bachman, William [mailto:bachmanw@globomax.com]
Sent: Friday, March 23, 2001 3:50 PM
To: Gibiansky, Leonid; KOWALSKI, KENNETH G. [PHR/1825]; 'diane r mould'
Cc: Gibiansky, Ekaterina
Subject: RE: Termination due to rounding errors
The only reference I have been able to find is in NONMEM V Supplemental Guide, p.1:
"2. Band Symmetric Matrices
An intial estimate of a diagonal block of either the OMEGA or SIGMA matrices may have a band symmetric form, in which case the final estimate had the same from."
Bill
-----Original Message-----
From: Gibiansky, Leonid
Sent: Friday, March 23, 2001 4:38 PM
To: 'KOWALSKI, KENNETH G. [PHR/1825]'; 'diane r mould'; Gibiansky, Leonid
Cc: Gibiansky, Ekaterina; Bachman, William
Subject: RE: Termination due to rounding errors
Katya tried it in our NONMEM V, and it worked exactly as Diane described Leonid
-----Original Message-----
From: KOWALSKI, KENNETH G. [PHR/1825]
[mailto:kenneth.g.kowalski@pharmacia.com]
Sent: Friday, March 23, 2001 4:36 PM
To: 'diane r mould'; Gibiansky, Leonid
Cc: Gibiansky, Ekaterina; Bachman, William
Subject: RE: Termination due to rounding errors
Diane,
Can you point to me where in the documentation in NONMEM V that allows banding...I can't seem to find it. Are you sure its not a feature of NONMEM VI which hasn't been released yet?
Thanks,
Ken
-----Original Message-----
From: diane r mould [mailto:drmould@attglobal.net]
Sent: Friday, March 23, 2001 2:44 PM
To: Gibiansky, Leonid
Cc: Gibiansky, Ekaterina; KOWALSKI, KENNETH G. [PHR/1825]; Bachman, William
Subject: Re: Termination due to rounding errors
Dear Leonid
Hi. Yes, I seem to recall seeing the documentation to BAND somewhere in the NONMEM manual, but when I looked for it just before my reply to NMUSERS, I could not find reference to it. Perhaps it was my imagination? I only learned about this feature recently and so can not say if it was available in NONMEM IV. It is certainly available in NONMEM V, however.
Yes, the construction of the BLOCK statement tells NONMEM whether or not you are using a BAND matrix. Your interpretation below is entirely correct. No fancy coding is required, although, as Tom Ludden has suggested, 'sometimes appropriate manipulation of the elements of the variance-covariance matrix are required'. I am not sure if he was specifically referring to this aspect of NONMEM or not but the idea was certainly apt.
Are you thinking of trying out BAND matricies? I have been very interested in learning more about other users experiences with trying to describe variance covariance terms. Some NONMEM users are strongly against describing this information, others feel strongly that it should be included. BAND matricies offer a useful alternative to those who wish to keep this information but find some elements poorly identifiable.
Best Regards
Diane
----- Original Message -----
From: "Gibiansky, Leonid" <gibianskyl@globomax.com>
To: "'diane r mould'" <drmould@attglobal.net>
Cc: "Gibiansky, Ekaterina" <gibianskye@globomax.com>; <kenneth.g.kowalski@pharmacia.com>; "Bachman, William" <bachmanw@globomax.com>
Sent: Friday, March 23, 2001 3:15 PM
Subject: RE: Termination due to rounding errors
> Dear Diane,
>
> Is this BAND feature documented somewhere ? Is it NONMEM VI feature
> unavailable in NONMEM V ? From what you wrote I understood that the initial
> values of OMEGA are somehow interpreted to create the OMEGA-BAND matrix ? Am
> I understood you correctly that:
>
> $OMEGA BLOCK(4)
> 10
> 1 10
> 1 1 10
> 1 1 1 10
>
> is interpreted as full 4 by 4 matrix;
>
> $OMEGA BLOCK(4)
> 10
> 1 10
> 1 1 10
> 0 1 1 10
>
> will keep (4,1)=(1,4) element equal to zero;
>
> $OMEGA BLOCK(4)
> 10
> 1 10
> 0 1 10
> 0 0 1 10
>
> will keep (4,1)=(1,4)= (3,1)=(1,3)=(2,4)=(4,2) elements equal to zero;
>
> $OMEGA BLOCK(4)
> 10
> 1 10
> 0 1 10
> 0 0 0 10
>
> will give an error that the matrix is not in the BAND form ?
>
>
> Thank you for your insight,
> Leonid
>