[R] Hessian from optim()
dimitris.rizopoulos at med.kuleuven.be
Tue Mar 21 17:56:19 CET 2006
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.
School of Public Health
Catholic University of Leuven
Address: Kapucijnenvoer 35, Leuven, Belgium
----- Original Message -----
From: "Ingmar Visser" <I.Visser at uva.nl>
To: "Thomas Lumley" <tlumley at u.washington.edu>; "Gregor Gorjanc"
<gregor.gorjanc at bfro.uni-lj.si>
Cc: <r-help at r-project.org>
Sent: Tuesday, March 21, 2006 5:41 PM
Subject: Re: [R] Hessian from optim()
>>> Looking on how people use optim to get MLE I also noticed that one
>>> use returned Hessian to get corresponding standard errors i.e.
>>> 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
>>> knowledge, but ... Attached PDF can show problem I am facing with
>> The Hessian is the second derivative of the objective function, so
>> if the
>> objective function is minus a loglikelihood the hessian is the
>> 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
>> just close (and there are in fact theoretical reasons to prefer the
>> observed information). I don't remember whether the two-parameter
>> family is one where the observed and expected information are
> The optim help page says:
> hessian Logical. Should a numerically differentiated Hessian
> matrix be
> I interpret this as providing a finite differences approximation of
> Hessian (possibly based on exact gradients?). Is that the case or is
> it a
> Hessian that results from the optimization process?
> Best, Ingmar
> R-help at stat.math.ethz.ch mailing list
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