Hi Bob, I don't have enough math to understand difference of those matrix, but, the final matrix output from nonmem was positive definite in my case
________________________________ From: Bob Leary <[email protected]> To: [email protected] Sent: Wednesday, February 25, 2009 8:33:53 AM Subject: RE: [NMusers] var-cov matrix issue? If S is singular, then the 'covariance' matrix Rinv * S * Rinv is also singular, as is the 'inverse coveriance matrix' R*Spseudoinv*R (the eigenvalues of Spseudoinv for the usual Moore Penrose pseudoinverse are the inverse of the eigenvalues of S, except where the S has a zero eigenvalue, in which case the corresponding eigenvalue of Spseudoinv is also zero. The eigenvectors are the same for S and Spseudoinv). Thus none of these quantities is really directly suitable for use in simulation if positive definiteness is a requirement. Robert H. Leary, PhD Fellow Pharsight - A Certara(tm) Company 5625 Dillard Dr., Suite 205 Cary, NC 27511 Phone/Voice Mail: (919) 852-4625, Fax: (919) 859-6871 Email: [email protected] > This email message (including any attachments) is for the sole use of the > intended recipient and may contain confidential and proprietary > information. Any disclosure or distribution to third parties that is not > specifically authorized by the sender is prohibited. If you are not the > intended recipient, please contact the sender by reply email and destroy all > copies of the original message. -----Original Message----- From: [email protected] [mailto:[email protected]]on Behalf Of Leonid Gibiansky Sent: Tuesday, February 24, 2009 15:59 PM To: Bachman, William Cc: Ethan Wu; [email protected]; [email protected] Subject: Re: [NMusers] var-cov matrix issue? According to the manual, covariance matrix IS calculated by the default method (Rinv S Rinv) even when S is singular but the inverse covariance matrix (R Sinv R) cannot be computed as usual since S is singular (see below). From the same manual "An error message stating that the S matrix is singular indicates strong overparameterization". If some of your OMEGAs are estimated with large error, I would try to remove those ETAs from the model. Scatter plot matrix of ETAs vs ETAs could be helpful: if some of your ETAs are redundant, you could see strong correlation of the ETAs estimates. -- The inverse variance-covariance matrix R*Sinv*R is also output (labeled as the Inverse Covariance Matrix), where Sinv is the inverse of the S matrix.. If S is judged to be singular, a pseudo-inverse of S is used, and since a pseudo-inverse is not unique, the inverse variance-covariance matrix is really not unique. In either case, the inverse variance-covariance matrix can be used to develop a joint con- fidence region for the complete set of population parameters. As we usually develop a confidence region for a very limited set of popula- tion parameters, this use of the inverse variance-covariance matrix is somewhat limited. -- -------------------------------------- Leonid Gibiansky, Ph.D. President, QuantPharm LLC web: www.quantpharm.com e-mail: LGibiansky at quantpharm.com tel: (301) 767 5566 Bachman, William wrote: > As a clarification, this is not an error. It is an indication of a > numerical condition generated by the matrix algebra. it says that the > covariance could not be calculated by the default method (possibly due > to ill conditioning) so it was calculated by an alternative method. You > could generate standard errors by an alternative method, e.g. bootstrap, > and compare them to those produced by NONMEM to make your decision to > trust or not trust the values. > > ------------------------------------------------------------------------ > *From:* [email protected] > [mailto:[email protected]] *On Behalf Of *Ethan Wu > *Sent:* Tuesday, February 24, 2009 2:09 PM > *To:* [email protected] > *Cc:* [email protected] > *Subject:* Re: [NMusers] var-cov matrix issue? > > Hi Justin, only ETA was estimated with high SE > but, again, I guess it came back to the question: how trustful it is if > such error message appears > > ------------------------------------------------------------------------ > *From:* "[email protected]" <[email protected]> > *To:* [email protected] > *Sent:* Tuesday, February 24, 2009 1:19:17 PM > *Subject:* Fw: [NMusers] var-cov matrix issue? > > > Dear Ethan, > > Algorithmically singular matrices are often a sign that that your model > is ill-conditioned in some way; I would be careful in how I used the > variance-covariance matrix in this scenario, and especially for > simulation. Are there any parameters that are being estimated with > particularly high standard errors? This might suggest overparamaterization. > > Not sure how helpful this is! > > Best > Justin > *Justin Wilkins > Senior Modeler** > Modeling & Simulation (Pharmacology)* > CHBS, WSJ-027.6.076 > Novartis Pharma AG > Lichtstrasse 35 > CH-4056 Basel > Switzerland > Phone: +41 61 324 6549 > Fax: +41 61 324 3039 > Cell: +41 76 561 0949 > Email : [email protected]_ <mailto:[email protected]> > > > > ----- Forwarded by Justin Wilkins/PH/Novartis on 2009/02/24 07:15 PM ----- > *Ethan Wu <[email protected]>* > Sent by: [email protected] > > 2009/02/24 07:12 PM > > > To > [email protected] > cc > > Subject > [NMusers] var-cov matrix issue? > > > > > > > > > Dear all, > I recently encounter this error message (below). My objective was to > use nonmem var-cov output for approximation of distribution of > parameters for performing a simulation. > if such error message occur, is the var-cov matrix still OK to use? > -- I know that better way to figure out distribution of parameters is to > do bootstrap, but given limited time I have..... > > thanks > > "0MINIMIZATION SUCCESSFUL > NO. OF FUNCTION EVALUATIONS USED: 331 > NO. OF SIG. DIGITS IN FINAL EST.: 3.3 > ETABAR IS THE ARITHMETIC MEAN OF THE ETA-ESTIMATES, > AND THE P-VALUE IS GIVEN FOR THE NULL HYPOTHESIS THAT THE TRUE MEAN IS 0. > ETABAR: 0..11E-02 > SE: 0.23E-01 > P VAL.: 0.96E+00 > 0S MATRIX ALGORITHMICALLY SINGULAR > 0S MATRIX IS OUTPUT > 0INVERSE COVARIANCE MATRIX SET TO RS*R, WHERE S* IS A PSEUDO INVERSE OF S > 1 > " > > ICON plc made the following annotations. > ------------------------------------------------------------------------------ > This e-mail transmission may contain confidential or legally privileged > information > that is intended only for the individual or entity named in the e-mail > address. If you > are not the intended recipient, you are hereby notified that any disclosure, > copying, > distribution, or reliance upon the contents of this e-mail is strictly > prohibited. If > you have received this e-mail transmission in error, please reply to the > sender, so that > ICON plc can arrange for proper delivery, and then please delete the message. > Thank You, > ICON plc > South County Business Park > Leopardstown > Dublin 18 > Ireland > Registered number: 145835 > >
