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

[Raquel Rangel de Meireles Guimarães <raquelrguimadem@gmail.com>]

Thank you Maarten for clarifying this.

Best,
Raquel

Raquel Rangel de Meireles Guimarães
PhD Student in Demography, Cedeplar/UFMG
MA Student in International Comparative Education, Stanford University
http://stanford.academia.edu/RaquelGuimaraes


Em 13/08/2011 09:06, Maarten Buis escreveu:
> 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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