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Re: st: mlogit estimation p-value problem


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: mlogit estimation p-value problem
Date   Wed, 12 Jun 2013 09:29:21 +0200

On Tue, Jun 11, 2013 at 1:54 PM, Andreas Chouliaras  wrote:
> First of all, why am I not using an ordered logit? Well, I believe
> that in an ordered logit, the odds of getting a value for the count
> equal to 5, instead of 4, are equivalent to the odds of observing 3
> instead of 2.

Close, but not quite: What is being modeled in an ordered logit is the
odds of 0 versus more than 0, 1 versus more than 1, etc.

> With such a constraint the estimates will be less less
> efficient if the odds are not proportional. And I don't think I have a
> strong reason why the odds should be proportional in my study.

The idea behind models like ordered logit or stereotyped ordered logit
is that you use assumptions to borrow information from observations
from adjacent categories. This way you gain efficiency. The price is
when your assumptions are wrong your results will be biased. So the
problem with an ordered logit is not a lack of efficiency but a
potential bias. In fact, an ordered logit will tend to be a lot more
efficient than a multinomial logit.

> Now, regarding the observations of outcome 5:
>
> bcW has 4 observations for outcome 5, tcW has 3 observations for
> outcome 5. I am putting the numbers of observations for outcome 5 for
> the other groups
>
> bcE : 18 tcE : 11
> bcP : 17 tcP : 12
> bcC : 41 tcC : 31

Trying to fit a -mlogit- on such small numbers of observations is
guaranteed to lead to hopelessly unstable results. So, given your
sample sizes you basically have two imperfect options: either you use
models like ordered logit to simplify your model enough such that you
get stable resutls or you collect more data and use that extra data to
stabelize your results.

A potential intermediate solution would be a generalized ordered
logit, which can relax the parallel regression assumption for some but
not all variables in your model. You can find out more about that
here: <http://www.nd.edu/~rwilliam/gologit2/>. However, given the
sample sizes you report I don't hold much hope.

Hope this helps,
Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

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