RE: OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS
Hi Jules,
If the correlation between two ETAs is 0 then you should be able to remove one
ETA and replace it by a scaled version of the other ETA and get the same
objective function value.
This model would not have a correlation problem (since only one ETA) so your
problem would be "solved" in a superficial way.
Of course you might not be satisfied with the idea that one of your ETAs is
(except for scale) wholly determined by the ETA for a different paramater with
a different physical interpretation.
What reason might be that these paramaters are so strongly related in your data?
I think that usually this suggests that the model is too complex for the
information available in the dataset. Or maybe some other model structure would
be better.
Douglas Eleveld
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Quoted reply history
Van: [email protected] [mailto:[email protected]] Namens
Jules Heuberger
Verzonden: September 17, 2013 12:42 PM
Aan: [email protected]
Onderwerp: [NMusers] OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS
Dear NM Users,
I ran into a problem with a NM 7.2 run with an OMEGA BLOCK (2), receiving an
error message saying the parameter estimate is near its boundary (See also the
discussion in [NMusers] How to solve it? ERROR: PARAMETER ESTIMATE IS NEAR ITS
BOUNDARY ). After digging through the documentation I am still unsure where the
problem is originating from. What I figured out is that the problem lies in the
OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS *******, a matrix I believe is
only introduced since NM7.2. The estimate in this matrix that is giving
problems is the one for the OMEGA BLOCK, which is estimated to be 1 (a
boundary).
Now, as far as I know, the OMEGA - CORR MATRIX is related to the OMEGA - COV
MATRIX as the sqrt of its estimate. However, it is unclear to me how the OMEGA
BLOCK estimate (COV MATRIX), which gives the correlation between the two ETAs,
is related to the OMEGA - CORR MATRIX value. What does this value actually
mean, and what does it mean for my error message, as the correlation estimate
itself seems to be fine? In the print below you can see the model and resulting
estimates, the important ones being 5.26E-02 (OMEGA - COV MATRIX of ETA1-ETA2)
and 1.00E+00 (OMEGA - CORR MATRIX of ETA1-ETA2). The model has two ETAs and an
proportional error model,
Thanks in advance for any insights and help,
Best,
Jules Heuberger
$SUB ADVAN=6 TOL=5
$MODEL
COMP=(CENTRAL)
COMP=(PERI)
$PK
; structural model
K10=IK10
V1 =IV1
K12=EXP(-1.29)
K21=EXP(-0.63)
V2=K12*V1/K21
BSL=IBSL
E0=THETA(1)*EXP(ETA(1))
EMAX=THETA(2)*EXP(ETA(2))
EC50=THETA(3)
;
$DES
DADT(1) = -K10*A(1)-K12*A(1)+K21*A(2)
DADT(2) = K12*A(1)-K21*A(2)
$ERROR
CP=F
EFF=E0-EMAX*F/(EC50+F)
Y= EFF*(1+ERR(1))+ERR(2)
IPRE=EFF
$THETA
55
20.9
364
;
$OMEGA BLOCK(2)
0.2
0.01 0.2
$SIGMA
0.01
0 FIX
$EST PRINT=5 MAX=9999 METHOD=1 INTERACTION POSTHOC NOABORT MSFO=mfi
__________________________________________________________
OMEGA - COV MATRIX FOR RANDOM EFFECTS - ETAS ********
ETA1 ETA2
ETA1
+ 2.44E-02
ETA2
+ 5.26E-02 1.13E-01
SIGMA - COV MATRIX FOR RANDOM EFFECTS - EPSILONS ****
EPS1 EPS2
EPS1
+ 1.11E-02
EPS2
+ 0.00E+00 0.00E+00
1
OMEGA - CORR MATRIX FOR RANDOM EFFECTS - ETAS *******
ETA1 ETA2
ETA1
+ 1.56E-01
ETA2
+ 1.00E+00 3.37E-01
SIGMA - CORR MATRIX FOR RANDOM EFFECTS - EPSILONS ***
EPS1 EPS2
EPS1
+ 1.05E-01
EPS2
+ 0.00E+00 0.00E+00
Jules Heuberger
Clinical Scientist
Centre for Human Drug Research
Zernikedreef 8
2333 CL Leiden
The Netherlands
'+31 (0)71 5246400
(+31 (0)6 43937461
7+31 (0)71 5246499
[email protected]<mailto:[email protected]>
http://www.chdr.nl/
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