Hello Bob,
If you can send a NONMEM $EST statement, which works better, it will be
greatly appreciated by the community! On my side, I'll try all proposed
solutions and share the outcome.
Thanks,
Pavel
On Thu, May 15, 2014 at 02:22 PM, Bob Leary wrote:
Hi Emmanuel,
While I am a strong advocate of using quasi-random rather than pseudo-
random sequences for importance sampling in EM methods like IMP, there
is a theoretical (and very real) problem with their use in the context
you suggested in your message, namely with a multivariate t
distribution as the importance sampling distribution. The 3S2 option
implies you are using a Sobol quasi-random sequence, while
the DF=7 implies the use of a multivariate T-distribution with 7 degrees
of freedom. The standard way of generating
a p-dimensional multivariate t -random variable with DF degrees of
freedom is to generate a p-dimensional multivariate normal and then
divide by an additional independent random variable which is basically
the square root of a 1-d chi square random variable with DF degrees of
freedom. Thus to generate a p-dimensional importance sample, you
actually need to use p+1 independent random variables. If you simply
use a p+1 dimensional Sobol vector as the base quasi-random draw, the
nonlinear mapping from p+1 dimensions to the final p dimensional result
destroys the low discrepancy property of the final sequence in the
p-dimensional space and in fact introduces a significant amount of bias
in the final result. The problem arises directly from the p+1 vs p
dimensional mismatch.
There is no problem if the final p-dimensional result can be generated
from a p-dimensional quasi-random sequence, which is the case for
multivariate normal
Importance samples. So quasi random sequences should really only be
used for the DF=0 multivariate normal importance sampling distribution
case, not the multivariate DF>0 multivariate t case.
I ran across this effect in testing the Sobol-based importance sampling
EM algorithm QRPEM in Phoenix NLME. It is very real and the net effect
is to introduce a significant bias. There is a partial fix that works
but gives up some of the benefit of using low-discrepancy sequences –
namely use a p-dimensional quasi-random vector to generate the
p-dimensional multivariate normal, but
then use a 1-d pseudo-random sequence to generate the chi-square random
variable.
From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com]
On Behalf Of Emmanuel Chigutsa
Sent: Thursday, May 15, 2014 1:03 PM
To: Pavel Belo; nmusers@globomaxnm.com
Subject: Re: [NMusers] SAEM and IMP
Hi Pavel
I have experienced a similar problem. In my case, the following code for
IMP after SAEM (using NM7.3) greatly reduced the Monte Carlo OFV noise
from variations of about +/- 60 points to variations of +/- 6 points
(though still not good enough for covariate testing):
$EST METHOD=IMP LAPLACE INTER NITER=15 ISAMPLE=3000 EONLY=1 DF=7
IACCEPT=0.3
ISAMPEND=10000 STDOBJ=2 MAPITER=0 PRINT=1 SEED=123456 RANMETHOD=3S2
The settings are explained in the NM7.3 guide. If you are using NM7.3,
you can also try IACCEPT=0.0 whereupon "NONMEM will determine the most
appropriate IACCEPT level for each subject". Of course the settings for
DF and IACCEPT in the above code will depend on the type of data you
have. Which brings me to my own question. If I have both continous and
categorical DVs in the dataset (which would mean different optimal
settings) and I am using F_FLAG accordingly, what would the 'right'
values of DF and IACCEPT be? I have noticed that the DF automatically
chosen by NONMEM for individuals in the dataset can vary from 0-8 and
this appears to be random.
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