Yes, recall if N -> large and the likelihood is regular the normal
approximation should be reasonable.
You could actually partly check this using the tools we discussed in the
section on standard errors. It's just a bit more complicated because it's a
multi-parameter model so you need to compute the profile likelihoods
(holding the nuisance parameters at their fixed MLE values), but that way
you could check if the quadratic approximation with the fisher information
is actually reasonable or not. No need to do this check here, but you could
if you are facing a similar question in practice.
Jens
-----Original Message-----
From: gov2001-l-bounces at
lists.fas.harvard.edu [mailto:gov2001-l-
bounces at
lists.fas.harvard.edu] On Behalf Of Jon Bischof
Sent: Saturday, April 12, 2008 5:49 PM
To: gov2001-l at
lists.fas.harvard.edu
Subject: Re: [gov2001-l] simulating probabilities
Quick followup: Are the taus distributed multivariate normal along
with the betas using variances from the Hessian?
Jon and Jane
On Sat, Apr 12, 2008 at 5:44 PM, Jens Hainmueller
<jhainmueller at gmail.com> wrote:
> When we are simulating the pooled expected
probabilities of yi*
> falling into any of the four categories, we need to simulate the
betas
> in order to get 1000 predicted yi*s.
However, if we use the
expected
> taus to determine which category each yi*
falls into, this seems
like
> an underestimate of the variance of the
expected probabilities
because
> the taus are also uncertain. Do we need to
simulate the taus as
well
and use a
new set of taus for every set of betas?
Yes, you need to draw and use all parameters (taus and betas) in the
simulation.
> PS--In part b of question 1, you ask us to simulate first
differences
> as COOP goes from 0 to 1. Did you mean 1 to
2 (COOP never equals
0)?
Yes thanks, I meant 1 to 2 (as indicated in the table below).
Corrected
version will be posted in a minute.
Hth,
Jens
-----Original Message-----
From: gov2001-l-bounces at
lists.fas.harvard.edu [mailto:gov2001-l-
bounces at
lists.fas.harvard.edu] On Behalf Of Jon Bischof
Sent: Saturday, April 12, 2008 5:30 PM
To: gov2001-l at
lists.fas.harvard.edu
Subject: [gov2001-l] simulating probabilities
Hey Jens,
Jon and Jane
_______________________________________________
gov2001-l mailing list
gov2001-l at
lists.fas.harvard.edu
http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l
_______________________________________________
gov2001-l mailing list
gov2001-l at
lists.fas.harvard.edu
http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l
--
Jon Bischof
Graduate Student
Department of Government
Harvard University
_______________________________________________
gov2001-l mailing list
gov2001-l at
lists.fas.harvard.edu
http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l