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Re: st: Prediction after a Xtlogit


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Prediction after a Xtlogit
Date   Wed, 16 Feb 2011 10:56:53 +0000 (GMT)

--- On Tue, 15/2/11, Milet Emmanuel wrote:
> How can marginal effects be calculated after a Xtlogit with
> the predict(pc1) option?
> Apparently it cannot - given the error message Stata
> delivers.

You have answered your own question.
 
> The other option, predict(pu0) can nonetheless be used. The
> only problem is that it assumes that the fixed effect is
> null - something that bothers me quite a lot actually.
> So, does anyone know a way to go around this difficulty ?

Yes, interpret your results in terms of odds ratios. What 
makes the effect of a continuous variable in a linear model
easy to interpet? An extra unit of x (the continuous variable)
will always lead to b (the coeficient) increase in the 
predicted of y (the dependent variable). This is true 
regardless of how much y one had to begin with. This is an
assumption that could be wrong, but it is the main strategy
that makes linear regression models so useful.

-(xt)logit- models use a similar strategy, here an extra 
unit of x leads to an increase or decrease of the expected
odds by a factor exp(b), regardless of how high the odds
was to begin with. So unlike marginal effects, you do not
need to know the values of the fixed effects, they just 
do not matter for the odds ratio.

For a similar argument (not surprising as I also wrote that 
one) see:
<http://www.stata.com/statalist/archive/2011-01/msg00123.html>

An alternative, would be to consider what you are doing 
when you compute marginal effect. You estimated a model that 
implies a non-linear effect on the probabilty and than you 
try to find some linear approximation of that effect. 
Basically, you are fitting a linear model on top of your 
non-linear model. If all you are going to do is interpet
the results of this linear model (i.e. the marginal effects)
then the obvious question would be: Why not cut out the 
middle man, and directly estimate a linear probablity model?
You would need to have some faith in the robustness of 
these models to violations of model assumptions, but with
marginal effects some awkward assumptions are also 
unavoidable. This is just to say that models aren't supposed
to be true, they are just supposed to be useful. But if these 
approximations bother you then you can always fall back on 
the odds ratio.
 
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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