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Re: st: Nominal or ordinal?


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Nominal or ordinal?
Date   Thu, 12 Aug 2010 23:00:35 -0500

At 08:30 PM 8/12/2010, Steve Samuels wrote:
Chelsea,  Ordinal logistic regression does require an assumption that
categories are "equally spaced".  Perhaps you are confusing ordinal
logistic regression with multiple regression on the category scores.

Steve

Steve, I am not sure I am following you (or if I do follow you I don't think I agree). According to the Stata 11 Reference Manual, p. 1273:

"The [proportional odds] model is based on the principle that the only effect of combining adjoining categories in ordered categorical regression problems should be a loss of efficiency in estimating the regression parameters."

So,take the original example, where the categories are (1) Not Likely, (2) Slightly Likely, (3) Quite Likely, (4) Extremely Likely. Suppose these are equally spaced. If the assumptions of the proportional odds model are met, you could combine categories 3 and 4, and the model would still work, albeit with less efficient estimation. Presumably the categories are no longer equally spaced then.

Perhaps I don't understand what you mean by "equally spaced" or maybe there is a major gap in my understanding, but I don't recall seeing an "equally spaced" requirement for ordinal regression; the outcomes just have to be ordered. (Of course, just because the outcomes are ordered does not mean the assumptions of the ordered logit model will be met, but that is a different issue.)


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Richard Williams, Notre Dame Dept of Sociology
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