I think it should be the first, since for BFGS and L-BFGS-B (the only optims()'s methods for which approximation to the hessian is required) it is known that the hessian update at convergence of the parameters might not yet be a good approximation of the true hessian.
Best, Dimitris ---- Dimitris Rizopoulos Ph.D. Student Biostatistical Centre School of Public Health Catholic University of Leuven Address: Kapucijnenvoer 35, Leuven, Belgium Tel: +32/(0)16/336899 Fax: +32/(0)16/337015 Web: http://www.med.kuleuven.be/biostat/ http://www.student.kuleuven.be/~m0390867/dimitris.htm ----- Original Message ----- From: "Ingmar Visser" <[EMAIL PROTECTED]> To: "Thomas Lumley" <[EMAIL PROTECTED]>; "Gregor Gorjanc" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Tuesday, March 21, 2006 5:41 PM Subject: Re: [R] Hessian from optim() > >>> Hello! >>> >>> Looking on how people use optim to get MLE I also noticed that one >>> can >>> use returned Hessian to get corresponding standard errors i.e. >>> something >>> like >>> >>> result <- optim(<< snip >>, hessian=T) >>> result$par # point estimates >>> vc <- solve(result$hessian) # var-cov matrix >>> se <- sqrt(diag(vc)) # standard errors >>> >>> What is actually Hessian representing here? I appologize for lack >>> of >>> knowledge, but ... Attached PDF can show problem I am facing with >>> this >>> issue. >>> >> >> The Hessian is the second derivative of the objective function, so >> if the >> objective function is minus a loglikelihood the hessian is the >> observed >> Fisher information. The inverse of the hessian is thus an >> estimate of >> the variance-covariance matrix of the parameters. >> >> For some models this is exactly I/n in your notation, for others it >> is >> just close (and there are in fact theoretical reasons to prefer the >> observed information). I don't remember whether the two-parameter >> gamma >> family is one where the observed and expected information are >> identical. > > > > The optim help page says: > > hessian Logical. Should a numerically differentiated Hessian > matrix be > returned? > > I interpret this as providing a finite differences approximation of > the > Hessian (possibly based on exact gradients?). Is that the case or is > it a > Hessian that results from the optimization process? > > Best, Ingmar > > ______________________________________________ > [email protected] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.html > Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
