Re: How serious are negative eigenvalues?

On 9/6/2010 1:27 PM, Bauer, Robert wrote: > Dieter: > You can trust the fit. The negative eignvalue diagnostic arises from > evaluating the information matrix of the estimates evaluated after the fit. > Because this was constructed with Monte Carlo components, on occasion the > slight imprecision from calculating obscure off-diagonal elements results in a > matrix that is not positive definite. An algorithm is used to shift the > eigenvalues slightly, and the following diagnostic > > Root mean square deviation of matrix from original= 1.37E-003 > > tells you how far the non-adjusted information matrix, multiplied by the > positive definite adjusted inverse matrix, differs from the Identity matrix. > Since this differs from the identity matrix only by 0.137% in your case, the > reported variance-covariance matrix, which is now positive definite, still > serves as a reasonable representation of the inverse of the information matrix, > despite the positive definiteness adjustment required. You can also visually > inspect the standard errors to see if these are reasonably sized. > > Alternatively, you can repeat the step: > > $EST METHOD=IMPMAP EONLY = 1 INTERACTION ISAMPLE=1000 NITER=5 FILE=IMP.EXT > > And because of slight Monte Carlo fluctuations is likely to give you a slightly > different result each time. If your root mean square deviation varies, or on > occasion you obtain a result without requiring the positive definiteness > adjustment, then this is another indicator that the negative eigenvalue result > is only the result of Monte Carlo fluctuations. > > Another method is to increase ISAMPLE to 3000, to reduce Monte Carlo > fluctuations. > > Robert J. Bauer, Ph.D. > Vice President, Pharmacometrics > ICON Development Solutions > Tel: (215) 616-6428 > Mob: (925) 286-0769 > Email: [email protected] > Web: www.icondevsolutions.com > > -----Original Message----- > From: [email protected] [mailto:[email protected]] On > Behalf Of Dieter Menne > Sent: Monday, September 06, 2010 12:11 PM > To: [email protected] > Subject: [NMusers] How serious are negative eigenvalues? > > Dear Nmusers, > > we have very rich data from MRI concentration measurements, with 11 > compartments and multiple compartments observed. The model is fit via SAEM > (nburn=2000), and followed by an IMPMAP as in the described in the 7.1.2 > manual. OMEGA is band with pair-wise block correlations in the following > style: > > $OMEGA BLOCK(2) > .02 ;CL > 0.01 0.06 ; VC > $OMEGA BLOCK(2) > 5.4 ; QMVP > 0.001 0.05 ;VMVP > $OMEGA BLOCK(2) > 0.06 ; QTVP > 0.001 0.25 ;VTPV > > $EST PRINT=1 METHOD=SAEM INTERACTION NBURN=2000 NITER=200 CTYPE=2 NSIG=2 > FILE=SAEM.EXT > $EST METHOD=IMPMAP EONLY = 1 INTERACTION ISAMPLE=1000 NITER=5 FILE=IMP.EXT > $COV PRINT=E UNCONDITIONAL > > Fits and CWRES diagnostics are perfect, and VPC checks are good. > > However, we have negative eigenvalues (the following example has been edited > by removing digits) > > ETAPval = 0.2 0.2 0.3 0.04 0.8 0.95 0.003 0.1 0.6 0.4 0.9 0.1 0.5 0.4 0.2 > 0.8 0.3 0.3 0.4 0.01 0.8 > ETAshr% = 13. 0.4 38 20 23 33 46 30 18 41 54 22 2. 26. 49. 12. 0.07 24. 18. > 35. 2.5 > EPSshr% = 7.5 8.1 > Number of Negative Eigenvalues in Matrix= 7 > Most negative value= -65339. > Most positive value= 88796185.9 > Forcing positive definiteness > Root mean square deviation of matrix from original= 1.37E-003 > > My question: can we trust this fit? > > Dieter Menne > Menne Biomed/University Hospital of Zürich > >