10 Mar
2009
10 Mar
'09
2:26 p.m.
What is the syntax to specify the bounds using L-BFGS-B. I've looked through the
R-help file but can't figure out how I tell optim what bounds to use....
From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l-bounces at
lists.fas.harvard.edu] On Behalf Of Lee, Clarence
Sent: Monday, March 09, 2009 10:44 PM
To: gov2001-l at lists.fas.harvard.edu
Subject: Re: [gov2001-l] EXO 1
I agree with Olena in that you need to use L-BFGS-B to get over that. My question is
more of a "good-standard" practice:
I notice that the problem to the reparametrization trick is that the SE's gets messed
up when we reparamterize - which seems to be a bit kludgy since usually we care about the
mean and the SE's. If reparamterization is a standard technique that most
statistician use, then is there a standard technique with BFGS that helps us find the SE?
(e.g. without specifying the bounds using L-BFGS-B)
Any insights?
Thanks,
Clarence
From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l-bounces at
lists.fas.harvard.edu] On Behalf Of Olena Ageyeva
Sent: Monday, March 09, 2009 8:46 PM
To: gov2001-l at lists.fas.harvard.edu
Subject: Re: [gov2001-l] EXO 1
I've got the same problem with re-parametrization and then I found out that instead
re-parametrization in this particular case we are advised to use L-BFGS-B method in
optim(), so we can set a lower and an upper limits for out point of interest. So, the
point of interest will never get out of this interval, which is sort of
reparameterization, right?
The section notes says that log-likelihood (I guess it's in general for any
LL-function?) is invariant to re-parametrization (any?), but I was not much successful
applying this technique for exponential log-likelihood function. With re-parametrization
done exactly the way it's in section note I get totally different result from what I
derived analytically.
As for pnorm(opt.1000 - 1.96*se) I think that it could be done separately for se and
opt.1000 - they both are found for reparameterized function. So, we basically looking for
opt and se in different coordinate system and then re-parameterized to get them back to
our original coordinate system. Am I right?
Sincerely,
Olena Ageyeva
Date: Mon, 9 Mar 2009 20:00:14 -0400
From: charlotte.cavaille at gmail.com
To: gov2001-l at lists.fas.harvard.edu
Subject: [gov2001-l] EXO 1
hi!
Quick (but fundamental question)
in exercise 1 gamma needs to be positive, so I re-parameterized...In
order to get the right MLE from optim() i didn't
forget to "re-parameterize" again...and i get the same result as the
one i found analytically. However, things change when i look for the
SE. Indeed, I get different answers analytically and with R (using the
hessian). I know this comes from the re-parameterization because I
don't have this issue when I change the whole function and do not
re-parameterize gamma. So my question is:
- if I re-parametterize, how do I apply the transformation to the
hessian to get the right result
how does that fit with the section notes that follows, why do we take
"pnorm" (this is the first transformation that is applied in the
ll.binom function) of "opt.1000 - 1.96*se" and not of "se" for
instance???
#binomial log-likelihood (N = # of trials for each observation)
ll.binom <- function(par, y, N){
# reparameterize pi; only search over [0,1]
p <- pnorm(par)
# log-likelihood
out <- sum(y*log(p) + (N-y)*log(1-p))
return(out)
}
# compare to wald ci
se <- sqrt(solve(-optim(par=2, fn=ll.binom, y=samp.1000, N=10,
method="BFGS",
control=list(fnscale=-1), hessian=T)$hessian)) #$
wald.ci <- c( pnorm(opt.1000 - 1.96*se), pnorm(opt.1000 + 1.96*se))
wald.ci # 0.7364839 0.7535663
- if i do not re-parameterize in order to be done with it and have
both my analytical
and my R result fit, how can i justify i am not re-parameterizing gamma?!
thanks!
charlotte
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