Condition number
Hello Ken:
I am quite unaware that some eigenvalues of a properly positive-definite
verified variance-covariance from a pure R matrix would be negative, or that
this would even occur for its correlation matrix.
Similarly, if the variance-covariance form is of sandwich form, such as
(Rinv)S(Rinv), if there components (R, S) were each verified to be positive
definite, then it, and its correlation matrix would necessarily have all
positive eigenvalues.
I would need to see your NONMEM result file to understand why this would
happen. Is the negative eigenvalues very small but negative? (such as 10^-15,
or something like that).
Robert J. Bauer, Ph.D.
Senior Director
Pharmacometrics R&D
ICON Early Phase
731 Arbor way, suite 100
Blue Bell, PA 19422
Office: (215) 616-6428
Mobile: (925) 286-0769
[email protected]<mailto:[email protected]>
http://www.iconplc.com/
Quoted reply history
From: Ken Kowalski <[email protected]>
Sent: Thursday, December 1, 2022 6:59 AM
To: Bauer, Robert <[email protected]>; [email protected]
Cc: 'Bonate, Peter' <[email protected]>
Subject: [EXTERNAL] RE: [NMusers] Condition number
Hi Bob,
Could it possibly be related to the S matrix and the default sandwich estimator
used in estimating the covariance and correlation matrices?
Ken
From: Ken Kowalski [mailto:[email protected]]
Sent: Thursday, December 1, 2022 9:52 AM
To: 'Bauer, Robert' <[email protected]>; [email protected]
Cc: 'Bonate, Peter' <[email protected]>
Subject: RE: [NMusers] Condition number
Hey Bob,
I get that NONMEM can encounter negative eigenvalues during the R matrix
decomposition and inversion step and if it does then the $COV step fails.
However, both Pete and I have encountered situations where the R matrix is
apparently positive definite since the $COV step runs but NONMEM reports a
negative eigenvalue from the correlation matrix from the PRINT=E option. It is
very rarely that I have seen this happen but it has happened to me. How can
this be if the R matrix is positive definite?
Thanks,
Ken
Kenneth G. Kowalski
Kowalski PMetrics Consulting, LLC
Email: [email protected]<mailto:[email protected]>
Cell: 248-207-5082
From: [email protected]<mailto:[email protected]>
[mailto:[email protected]] On Behalf Of Bauer, Robert
Sent: Wednesday, November 30, 2022 1:53 PM
To: '[email protected]'
<[email protected]<mailto:[email protected]>>
Subject: RE: [NMusers] Condition number
Hello all:
Report of non-positive definiteness or negative eigenvalues, are reported
during the analysis of the R matrix (decomposition and inversion), which occurs
before the correlation matrix is constructed. Often, this is caused by
numerical imprecision. If the R matrix step fails, the $COV step fails to
produce a final variance-covariance matrix, and of course, does not produce a
correlation matrix. If the R matrix inversion step succeeds, the
variance-covariance matrix and its correlation matrix are produced, and the
correlation matrix is then assessed for its eigenvalues. So, both the R matrix
(first step) and correlation matrix (second step) are decomposed and assessed.
Robert J. Bauer, Ph.D.
Senior Director
Pharmacometrics R&D
ICON Early Phase
731 Arbor way, suite 100
Blue Bell, PA 19422
Office: (215) 616-6428
Mobile: (925) 286-0769
[email protected]<mailto:[email protected]>
http://www.iconplc.com/