RE: How serious are negative eigenvalues?

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