Re: 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 > " > >