RE: OMEGA HAS A NONZERO BLOCK
From:Leonid Gibiansky
Subject:RE: [NMusers] OMEGA HAS A NONZERO BLOCK
Date:Mon, 07 Oct 2002 16:40:42 -0400
Shouldn't we agree that there are no absolute rules that fit all the cases?
Suppose that you have an ill posed problem, with correlation close to one;
when you try to fix correlation to 0.5, OF increases, fit become worse.
Profiling of the OF evidence that, given the data, correlation=1
corresponds to the minimum. There are no strong prior information that
correlation should not be equal to one. Bootstrap show distribution of
correlation coefficients centered somewhere near 0.9.
I would put correlation to 1. Is there any reasons not to do it ? Prior
information should be very strong and reliable in order to shift the
balance from the data in hand to the prior data: if we would be so
confident in the prior information, why would we do a new analysis ?
On the other hand, if in the similar situation:
OF profile is very shallow with no difference between correlation = 1 and
correlation = 0,
bootstrap gives distribution close to the uniform, and
no prior information is available,
I would put correlation to zero.
Instead of bootstrap and profiling, which require a lot of efforts, one can
look on the standard errors of the correlation coefficient. If SE is small
- then the true parameter value is likely to be equal to the NONMEM
estimate. If SE is very high one can fix the parameter to any value (I
would not use 0.5, I prefer 0 or 1, but this can be a matter of taste). For
OMEGA-block size >3, it is hard to get standard errors for the correlation
coefficients from NONMEM. Then parameterization that I propose earlier may
help: it is straightforward to obtain standard errors for THETAs, and those
thetas characterize correlation of the parameters.
Prior knowledge may shift balance in either direction for the situation 2.
An intermediate situations can be decided on the case by case basis
weighing the balance of prior knowledge, new data, time to the final
report, etc.
Leonid