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st: Proportional Odds Assumption


From   "Brooks Taggert J" <brooks.tagg@uwlax.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Proportional Odds Assumption
Date   Mon, 14 Dec 2009 09:02:05 -0600

My apologies in advance as this is not precisely a Stata question.
Though I'm quite sure I can use Stata to help answer it.

I'm estimating an ordered logit -ologit - in Stata, since my dependent
variable is final class letter grade. I realize the strong proportional
odds assumption of the model, ie parallel regressions, and test for
those using Long and Freese's -brant- test. I also use Wolfe and Gould's
-omodel- as well. I find that the strong assumptions are in fact too
strong, and therefore turn to - slogit - proposed by Anderson (1984) to
estimate different coefficients between outcome categories (actually
different scaling factors for the coefficients).  My question is rather
simple. I want to say something about the type of mistake one makes when
merely using the -ologit- results in this case. Obviously the
coefficient estimates are wrong, but I can't find a paper that suggests
how and in what ways they might be wrong. Kim (2003) argues that even if
the test of -omodel- finds a statistically significant departure from
parallel regressions it might not be practically significant. I'm
wondering if anyone has a citation investigating the ways in which
-ologit- might be misrepresenting the coefficient estimates. I have some
sense that it is forced to use the "average" of what -slogit- might
produce, but I can't confirm that. Maybe it is some weighted average?
The reason is I want to be able to articulate the inappropriate
inference that is made when incorrectly using the -ologit- coefficients.

Clearly the precise quantity is off, but what if that is of secondary
importance to the research relative to the sign and significance for the
researcher when making inference?

Any thoughts would be much appreciated.

TJ

Anderson, J. A. (1984). Regression and Ordered Categorical Variables.
Journal of the Royal Statistical Society. Series B (Methodological),
46(1), 1-30.

Kim, J.-H. (2003). Assessing practical significance of the proportional
odds assumption. Statistics & Probability Letters, 65(3), 233-239.

Taggert J. Brooks, PhD
Associate Professor
Department of Economics
University of Wisconsin - La Crosse




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