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RE: st: Test of ordered probit vs ordinary probits


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu, <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Test of ordered probit vs ordinary probits
Date   Thu, 01 Nov 2007 08:56:39 -0500

At 06:14 AM 11/1/2007, Schaffer, Mark E wrote:
This takes me back to my original example of a bunch of separate
probits, but this time contrasted with, e.g., the default behavior of
-gologit2- (with link(pr) to make it a generalized ordered probit).  The
latter imposes only the constraint that the cutoffs are ordered,
corresponding to order-ability of the outcome variable.  How would you
test this constraint?
Actually, an unconstrained gologit doesn't even impose that constraint. Indeed, Clogg argued that the model isn't ordinal (or at least need not be ordinal). You can even rearrange the categories of Y and still get about the same fit! Since unconstrained gologit has as many parameters as mlogit, this actually isn't that surprising.

This handout talks about possible interpretations of a gologit model:

http://www.nd.edu/~rwilliam/gologit2/RWNASUG2006.pdf

One of the ideas tossed out is that the same Y could be ordinal in different ways, e.g. it might be ordered Strongly Disagree to Strongly Agree; or it might be ordered indifferent to feel strongly (either agree or disagree). For some independent vars, the first ordering may be appropriate, but for others the 2nd ordering may be appropriate.

This isn't really answering your question. But, informal checks, I think, would include looking for sign flips across equations. Usually, differences in coefficients across equations are just a matter of degree (e.g. they're all positive but differ in magnitude) but if you see them changing sign then that suggests the relationship is not ordinal or perhaps differently-ordinal (i.e. the var should be coded differently, as I suggest above).



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Richard Williams, Notre Dame Dept of Sociology
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