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: robert.ba...@iconplc.com Web: www.icondevsolutions.com -----Original Message----- From: owner-nmus...@globomaxnm.com [mailto:owner-nmus...@globomaxnm.com] On Behalf Of Dieter Menne Sent: Monday, September 06, 2010 12:11 PM To: nmusers@globomaxnm.com 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 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
