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Re: [NMusers] Zeros in OMEGA matrix

From: Leonid Gibiansky <lgibiansky_at_quantpharm.com>
Date: Fri, 03 Jul 2015 15:56:06 -0400

You may define

MYETA1 = C11*ETA(1)
MYETA2 = C12*ETA(1)+C22*ETA(2)
MYETA3 = C23*ETA(2)+C33*ETA(3)
MYETA4 = C24*ETA(2)+C34*ETA(3)+C44*ETA(4)

with diagonal (and fixed to unit matrix) OMEGA matrix of ETA(1:4)

Then OMEGA for MYETA[1:4] matrix is

C11*C11
C11*C12 C12*C12+C22*C22
    0 C22*C23 C23*C23+C33*C33
    0 C22*C24 C23*C24+C33*C34 C24*C24+C34*C34+C44*C44

I am not sure whether it makes sense to go that far to get an extra 0 or
extra flexibility (relative to the band matrices with 1 or 3 zeros), but
technically, this is equivalent to the matrix that you need.

Another (simpler) option is to define

MYETA1 = ETA(1)
MYETA2 = ETA(2)
MYETA3 = ETA(3)
MYETA4 = ETA(4)+C24*ETA(2)

with the band matrix for ETAs:

Sw
C(w,x) Sx
0 C(x,y) Sy
0 0 C(y,z) Sz

The term C24*ETA(2) will add extra correlation (2-4) for MYETA matrix
that is forbidden by the band matrix for ETA(1:4).

Leonid

--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566



On 7/3/2015 9:58 AM, Gavin Jarvis wrote:
> Dear NMUsers
>
> I have a problem and hope someone might be able to help. In summary, is
> it possible for NONMEM to model an OMEGA matrix with four elements
> (W,X,Y,Z) such that two of the covariances are fixed to zero and the
> rest freely determined? I realise NONMEM can model BAND matrices, but I
> canít see how to fix just two covariances to zero. The final matrix
> structure Iím looking for would look something likeÖ
>
> Sw
>
> C(w,x) Sx
>
> 0 C(x,y) Sy
>
> 0 C(x,z) C(y,z) Sz
>
> I hope that makes sense. If so, is it possible?
>
> Many thanks
>
> Gavin
>
> __________________________________________________
>
> *Dr Gavin E Jarvis MA**(Cantab)**MA PhD VetMB MRCVS*
>
> University Lecturer in Veterinary Anatomy
>
> Department of Physiology, Development & Neuroscience
>
> Physiological Laboratory
>
> Downing Street
>
> Cambridge
>
> CB2 3EG
>
> Tel: +44 (0) 1223 333745
>
> Fellow and College Lecturer in Pharmacology
>
> Tutor for Graduate Students
>
> Selwyn College
>
> Cambridge
>
> CB3 9DQ
>
> Tel: +44 (0) 1223 761303
>
> Email: gej1000_at_cam.ac.uk <mailto:gej1000_at_cam.ac.uk>
>
> Web: www.pdn.cam.ac.uk/staff/jarvis <http://www.pdn.cam.ac.uk/staff/jarvis>
>
> Twitter: _at_GavinEJarvis
>
Received on Fri Jul 03 2015 - 15:56:06 EDT

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