Re: st: Nominal or ordinal?

[Richard Williams <richardwilliams.ndu@gmail.com>]

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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