Thanks for the discussion! Some literature indeed would suggest not too focus too much on the sandwich estimator (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.8.5787&rep=rep1&type=pdf) certainly not in situations where the sample size is ‘small’ and when leverage points are encountered. The notions about bias (http://www.stat.berkeley.edu/~census/mlesan.pdf) may be even more important and the suggestion by http://www.polmeth.wustl.edu/media/Paper/robust.pdf seems worthwhile to try (I at least never did – anyone?): they suggest to compare the sandwich estimator with the Hessian (classical) one. A difference between the two could be used as a diagnostic pointing to some model misspecification.
Jeroen From: [email protected] [mailto:[email protected]] On Behalf Of Bauer, Robert Sent: Saturday, March 29, 2014 21:46 To: Kowalski, Ken; 'Gavin Jarvis'; [email protected] Subject: RE: [NMusers] NONMEM vs SPSS I concur with Ken’s statement, and I also prefer to use MATRIX=R as the first choice for covariance assessment. On occasion, MATRIX=S can be used if there are numerical difficulties in assessing the R matrix, and if there are enough subjects relative to the dimension size (number of total parameters estimated) of the variance-covariance matrix to be estimated. Robert J. Bauer, Ph.D. Vice President, Pharmacometrics, R&D ICON Development Solutions 7740 Milestone Parkway Suite 150 Hanover, MD 21076 Tel: (215) 616-6428 Mob: (925) 286-0769 Email: [email protected]<mailto:[email protected]> Web: www.iconplc.com<http://www.iconplc.com/> From: [email protected]<mailto:[email protected]> [mailto:[email protected]] On Behalf Of Ken Kowalski Sent: Saturday, March 29, 2014 3:44 PM To: 'Gavin Jarvis'; [email protected]<mailto:[email protected]> Subject: RE: [NMusers] NONMEM vs SPSS Dear Gavin, This is most likely because most nonlinear regression programs invert the Hessian (second derivative matrix of the model with respect to the parameters) to obtain the covariance matrix. This corresponds to the R matrix in NONMEM. However, the default method that NONMEM uses is a sandwich estimator involving both the Hessian (R) and the square of the first derivatives matrix (S). I suspect that if you use the MATRIX=R option on the $COV step you will find that the standard errors will now be in agreement with SPSS (NLR). I know Stu Beal made the sandwich estimator the default as it is supposed to be more robust to non-normality but I would have preferred the MATRIX=R option to be the default to be more consistent with other nonlinear regression software implementations. Ken From: [email protected]<mailto:[email protected]> [mailto:[email protected]] On Behalf Of Gavin Jarvis Sent: Saturday, March 29, 2014 12:55 PM To: [email protected]<mailto:[email protected]> Subject: [NMusers] NONMEM vs SPSS Dear NONMEM Users Does anyone have a view on the relative merits/reliability/accuracy of NONMEM ($COV step) vs SPSS (NLR) with respect to their derived values of the parameter standard errors and parameter correlation matrices? The data I am analysing are single subject (not population). Parameter estimates from the two programs are, to all intents and purposes, identical. However, the SE values from NONMEM $COV are consistently smaller by 1.5-2.0-fold. Any thoughts? Gavin __________________________________________________ Dr Gavin E Jarvis MA PhD VetMB MRCVS University Lecturer in Veterinary Anatomy Department of Physiology, Development & Neuroscience Physiological Laboratory Downing Street Cambridge CB2 3EG Tel: +44 (0) 1223 333745 Fellow and College Lecturer in Pharmacology Selwyn College Cambridge CB3 9DQ Tel: +44 (0) 1223 761303 Email: [email protected]<mailto:[email protected]> Web: www.pdn.cam.ac.uk/staff/jarvis<http://www.pdn.cam.ac.uk/staff/jarvis> Twit: @GavinEJarvis 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 Notice: This e-mail message, together with any attachments, contains information of Merck & Co., Inc. (One Merck Drive, Whitehouse Station, New Jersey, USA 08889), and/or its affiliates Direct contact information for affiliates is available at http://www.merck.com/contact/contacts.html) that may be confidential, proprietary copyrighted and/or legally privileged. It is intended solely for the use of the individual or entity named on this message. If you are not the intended recipient, and have received this message in error, please notify us immediately by reply e-mail and then delete it from your system.
