Re: st: test for appropriateness of logit models

["Joseph Coveney" <stajc2@gmail.com>]

Maarten Buis wrote:

On Sat, Jun 15, 2013 at 1:21 PM, Andreas Chouliaras wrote:
> I would like to apply a test to check the appropriateness of a
> multinomial vs an ordered logit model (or another flavor such as
> gologit2).

It would make most sense to compare an ordered logit with a full free
generalized ordered logit. After a gologit a mlogit would make little
sense; an mlogit would describe the pattern with the exactly same
number of parameters, the difference is only which outcome categories
are compared. Richard Wiliams and I discussed at the last German Stata
Users' meeting the different tests that are available for testing an
ologit against a gologit. The slides can found here:
http://www.maartenbuis.nl/presentations/gsug13.pdf

---------------------------------

I wonder if Andreas is referring to a situation where, say, a three-category
response variable is said  to be conceptually ambiguous (or is controvertible)
as to whether the categories are ordered or not.  Something like "A", "B", and
"some characteristics of A/some characteristics of B".  Some subject-matter
experts might be inclined to consider the response variable as representing
B-ness (or A-ness), and the scores run from "none or a little" to "some" to "a
lot or all".  While others view it as nominal, with scores of A, B and "not
really either".

It seems that generalized ordered logistic regression could suggest a principled
approach to these situations.  For example, after considering Richard Williams's
July 2006 follow-up presentation on -gologit2- (see links at
http://www3.nd.edu/~rwilliam/gologit2/ ), maybe you can first determine whether
you end up with unacceptable negative predicted probabilities with relaxed
constraints, and if not, then determine whether the totally unconstrained model
is the "best fit" according to one or another criterion, and if so then toss a
coin to decide whether to just use -mlogit- with a convenience choice of
baseline score.  (This abbreviated example of course doesn't take into account
matters of response dimensionality and heterogeneity that Richard Williams
describes in his presentation.)

Do list members have alternative advice as to how to approach analysis in these
situations based upon what's worked for them?  Perhaps it boils down to the
nitty-gritty details of the specific research question being addressed (which
would be a safe answer), and there's no generally applicable protocol for
approaching these situations.

Joseph Coveney

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