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st: RE: Help with mlogit questions; IIA; choosing outcome variables; collapsing outcomes, multinomial logistic regression


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Help with mlogit questions; IIA; choosing outcome variables; collapsing outcomes, multinomial logistic regression
Date   Thu, 14 May 2009 14:06:55 -0400

Tomas M wrote: 


>>QUESTION: Suppose that the mlogtests give results that suggest that
the alternatives (i.e. outcomes) CAN be combined (i.e. gives a high
p-value for evidence for the null, as stated above), does this mean that
if we choose to combine the alternatives, we can do so in the model? (if
we choose to combine them based on our knowledge of the data, etc.). Or
does this mean that we SHOULD combine the alternatives?<<

The answer to "Should these be combined?" seems to depend on "What point
are you trying to make?" 

Merging serves two purposes, one statistical (cut df) and the other
model parsimony. The mlogit model is quite complex so if you can make
your point with fewer categories that may be wise. However, it's hard to
answer this without a lot more context. I would be very wary of merging
categories in a way that isn't sensible regardless of what the
statistical tests say.  



>>OTHER QUESTION: Suppose I have the following outcome variables: blue
collar, white collar, professional, no job. How would I go about
deciding whether to include "No job" as an outcome in my models? Suppose
that having "No Job" included in my models, versus having it excluded,
makes no difference to the estimated coefficients.  What justifications
should I use to decide whether to include "No Job" or exclude it?  Is
this solely a decision based on my own knowledge of the data, and
whether or not it would be of interest to the readers?<<

Not including a category may alter the population you're studying so you
should be really careful. Dropping no job makes the sample conditional
on being employed, which is a different population. 



>>Does the assumption of independence of irrelevant alternatives (IIA)
have anything to do with this justification?  I.e., if all of my
outcomes satisfy this assumption (after running the Hausman and/or
Small-Hsiao tests), and they are distinct and dissimilar, then it does
not matter if I include "No Job" or not (and thus my choice for
including or excluding it rests solely on my decisions as an analyst)?<<

With collapsing categories? Yes, one way to make things closer to IIA
and thereby avoid the use of more complex models such as mixed logit is
to get rid of categories that are highly similar. See Red Bus/Blue Bus
Problem. 

JV



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