Re: Problems with an apparent compiler-senstive model
From: Mark Sale - Next Level Solutions mark@nextlevelsolns.com
Subject: Re: [NMusers] Problems with an apparent compiler-senstive model
Date: Wed, 02 Aug 2006 08:52:44 -0700
Lenoid,
I, for one am not ready to discard convergence as a measure of model
"goodness". I'm not even prepared to discard covariance success as a
measure of model "goodness" - everything else being equal I will always
prefer a model that converges|does a covariance step over one that
doesn't. But, at the same time, I'd suggest that covariance step or
convergence isn't required to deem a model useful (as we all know, they
are never correct), or even final. The hard choices are when a model
that makes biological sense refuses to converge and simple, empirial
models do converge.
Next, there are, I beleive three factors that contribute to "model
instability" (meaning that the variance/covariance matrix cannot be
inverted and/or the model fails the internal criteria for NONMEM to
declare it converged. These three factors overlap greatly, and are
very rarely black and white. They are:
1. Model dependent non-identifiability - your example, you cannnot,
regardless of the amount/quality of the data identify CL, V and F with
only oral data. (although I had an example where NONMEM converge
successfully in such a case - supporting Nicks position). Essentially,
any value of F is consistent with the data (with a corresponding value
for CL and V). In this case, I beleive that the condition number/rank
of the covariance matrix would indicate this.
2. Data dependent non-identifiability. Imagine that you want to
estimate KA, but all of your data is in the terminal phase. Basically
any value of KA is consistent with the data (therefore, the likelihood
of the data isn't effected by the value of KA, the objective function
surface is flat in that dimension). This will be true regardless of
the quality of the data. In this case as well, I beleive that the
condition number/rank of the covariance matrix would indicate this.
Note the same root cause as data dependent non-identifiability - any
value of a parameter is consistent with the data.
3. Numerical problems. Much more vague concept. Partly related to
"quality" of the data (model misspecification, residual error, auto
correlation). But, also includes true rounding errors, which are most
likely to be seen if we have a wide range of likelihoods between
subjects (e.g., some individuals have a lot of data, some have little
data). But, this source of rouding error is probably small compared to
the model misspecification, large residual error and autocorrelation.
Auto correlation, BTW, is known to be very, very bad in linear
regression - resulting in bias in both parameter estimates and
estiamtes of SE. I'm not aware that it has been studied much in
non-linear regression, but I suspect it is a significant problem, only
partly addressed by the L2 variable.
Mark Sale MD
Next Level Solutions, LLC
www.NextLevelSolns.com