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# Re: st: Formal question: multinomial logit vs separate classical logit

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: Formal question: multinomial logit vs separate classical logit Date Sat, 13 Aug 2011 14:06:58 +0200

```2011/8/12 Raquel Rangel de Meireles Guimarães:
> I am estimating a multinomial logit model with 4 categories (consider that
> reference category is #4).
>
> My question is: If I estimate 4 separate binomial logit models:
>
> P(Y=1) when the reference category is #4
> P(Y=2) when the reference category is #4
> P(Y=3) when the reference category is #4
>
> Formally it can be assured that P_hat(Y=4)=P_hat(Y=1)-P_hat(Y=2)-P_hat(Y=3)?
> Or it is a wrong specification?

The difference between -mlogit- and three separate -logit-s is that
-mlogit- will also include the constraint that the 4 probabilites add
up to 1. The separate logit do not enforce that constraint. How could
they when they are estimated separately? In practice the probabilities
will be close to adding up to 1 as long as you are not extrapolating.
However, this could be a real problem when extrapolating.

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

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

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