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st: Fwd: Simulating Multinomial Logit in Stata


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Fwd: Simulating Multinomial Logit in Stata
Date   Tue, 14 May 2013 10:36:14 +0200

--- 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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