From:"Rajanikanth Madabushi" rajanim@ufl.edu
Subject:[NMusers] Initial estimates query
Date: Mon, Oct 16, 2003 10:43 am
Hi all,
I have a query regarding the initial estimates for the thetas we give. Good
initial estimates are necessary for avoiding convergence to local minima.
Suppose a set of initial estimates converge with an increased objective
function value and the parameter estimates appear more realistic and another
set of intial estimates lead to convergence with a lower objective function
but unrealistic estimates. I feel that one should choose a parsimonous
model which would give consistent estimates with changes in the value of
initial estimates. Is it the right approach??? How dependent should a
model be on the value of the initial estimates?
thanking in advance
Raj
Initial estimates query
From: "Bachman, William" bachmanw@globomax.com
Subject: RE: [NMusers] Re: Initial estimates query
Date: Thu, October 16, 2003 11:26 am
How dependent should a model be on the value of the initial estimates?
ideally not at all! (however, that glib response does not reflect reality)
You are putting too much importance in the objective function value. Also
consider goodness of fit (your "realistic estimates"?) and the magnitude of
the variance estimates.
It is possible to have a higher objective function value for a run with
"realistic estimates" than a run with "non-realistic estimates",
particularly if NEITHER represents the global minimum. I would approach
this conundrum by trying multiple sets of initial estimates to try to hone
in on the global minimum. Depending on the nature of your data, it is
possible to have a relatively "flat", featureless or just plain bizarre
response surface that makes it more or less impossible to achieve a global
minimum. At that point, take into consideration the intended use of your
model and then, if allowable as determined by the model use, go with the
"best" parameter estimates you obtained. If the use does not permit this
"relaxed" approach, you are just out of luck. Do a new study, get better
data.
Bill
From: Jeff Wald, PhD jeffrey.a.wald@gsk.com
Subject: RE: [NMusers] Re: Initial estimates query
Date: 10/16/2003 2:03 PM
Whenever I see the word realistic enclosed by quotes, I start to think it is a
problem for Reverend Bayes. He has done some nice work characterizing the
continuum of Unrealistic - "Unrealistic" - "Realistic" - Realistic ;-)
Jeff
Jeff Wald, PhD
jeffrey.a.wald@gsk.com
Clinical Pharmacokinetics/Modeling and Simulation
RTP, NC
From: "Kowalski, Ken" Ken.Kowalski@pfizer.com
Subject: RE: [NMusers] Re: Initial estimates query
Date: Fri, October 17, 2003 7:42 am
Jeff, All,
Yes, whenever I hear one say that a certain set of estimates are realistic
and another set is not, this suggests the modeler has prior information. If
one is in a situation where convergence is overly sensitive to starting
values (a symptom of ill-conditioning) leading to local minima we have
several choices:
1) Collect more data as Bill suggests.
2) Make better use of prior information (e.g., perform a Bayesian analysis,
fix certain estimates based on independent information, etc.)
3) Simplify the model perhaps accepting a less mechanistic one if it meets
the objectives and intended use of the model.
In my opinion, all three strategies above are better than accepting a model
with "realistic" estimates at a known local minimum (i.e., higher OFV than
for another set of feasible but "un-realistic" estimates).
Ken
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