RE: Help: Non-positive semi-definite message
From: "KOWALSKI, KENNETH G. [R&D/1825]" <kenneth.g.kowalski@pharmacia.com>
Subject: RE: Help: Non-positive semi-definite message
Date: Tue, 21 Aug 2001 09:55:07 -0500
Nick,
>I recall your talk which was very helpful at pointing to solutions to the
>problem. The importance of knowing something about covariance when doing
>simulations needs to be continuously emphasized. While using a covariance
of >1 may not be as harmful as a covariance of 0 it still seem that we would
be
>better off with a middle position which uses some covariance between 0 and
1.
>Do you have any specific comments on the method I suggested?
>$OMEGA 1 ; CL
>$OMEGA 1 ; V
>$OMEGA .09 FIXED ; COV
> CL=THETA(1)*EXP(ETA(1))
> V=THETA(2)*EXP(ETA(3)*ETA(1))
In the setting when NONMEM wants to estimate the correlation for an
off-diagonal element of omega to 1 what value do you propose fixing the
covariance value to? If you fix the covariance at various values (and
estimate everything else) I believe you will find that the minimum OFV will
correspond to the estimate of the covariance which leads to the correlation
being set to 1.0. Thus, any fixed value that results in the correlation
being constrained to less than 1.0 should have a higher OFV and hence will
be less parsimonious. I don't know how one arbitrarily sets the correlation
to be something between 0 and 1 when the data/design do not provide
sufficient information to estimate it different from 1. If you set it
arbitrarily close to 1 like 0.95 or 0.99 so as not to increase the OFV too
much then you have a "near perfect correlation" and your concern would still
exist at least approximately.
Ken