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st: Fwd: Simulating Multinomial Logit in Stata

From   Maarten Buis <>
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:
> 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:

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

-- Maarten

Maarten L. Buis
Reichpietschufer 50
10785 Berlin
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