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st: AW: Fwd: Simulating Multinomial Logit in Stata


From   "Klaus Pforr" <kpforr@googlemail.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: AW: Fwd: Simulating Multinomial Logit in Stata
Date   Tue, 14 May 2013 12:13:37 +0200

<>

You should note, that the error terms for each alternative equation are
identically, independent gumbel-distributed -- as Maarten wrote -- and that
therefore the comparison-pairs alternative 1 vs. base-alternative, ...,
alternative J-1 vs. base-alternative are identically, independent
logistically distributed. See the english wiki-page (or any statistics
textbook) for this relationship.

And I would like to add to Maarten's general recommendation, that individual
requests that follow from a statalist post are short of annoying. IMHO
statalist is not a TA-speeddating-platform.

Klaus

-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Maarten Buis
Gesendet: Dienstag, 14. Mai 2013 10:36
An: statalist@hsphsun2.harvard.edu
Betreff: st: Fwd: Simulating Multinomial Logit in Stata

--- andrea capre wrote me privately:
> I am writing to ask a question related to this post:
>
> http://www.stata.com/statalist/archive/2013-03/msg00535.html
>
> When one simulates a multinomial logit model by computing the 
> probabilities and then simulating random uniform (0,1) numbers as you 
> do in the statalist post, what is the variance that the error term 
> has?  (the variance of the extreme value e_ij in the random utility model
which precedes the multinomial logit:
> u_ij=xb+e_ij

Questions like these are best sent to the Statalist rather than its
individual members. The reasons are discussed here:
<http://www.stata.com/support/faqs/resources/statalist-faq/#private>

In a multinomial logit you will have multiple error terms, 1 for each
equation/comparison of outcomes. These error terms are uncorrelated (that is
an other way of saying the IIA assumption holds), follow a gumbel
distribution with mu=0 and \beta = 1 such that the PDF is:
exp(-e - exp(-e)), and the variance of each of these error terms is
(pi^2)/6.

-- Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------
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