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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 --------------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Fwd: Simulating Multinomial Logit in Stata***From:*Maarten Buis <maartenlbuis@gmail.com>

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