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Re: st: Nominal or ordinal?


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Nominal or ordinal?
Date   Fri, 13 Aug 2010 10:32:08 -0400

At 08:42 AM 8/13/2010, Ronan Conroy wrote:
On 12 Lún 2010, at 21:29, David Bell wrote:

Most of the world is willing to treat scales like this as interval
data.  Sure it isn't "exactly" interval.  Be sure to consider
whether your audience will be familiar with interpretations of
ordinal logit regressions.

I cannot endorse the behaviour of most of the world, which is usually
characterised more by wishful thinking than by reflection.

The assumption of normally distributed error is broken for short
ordinal scales, and I refuse to believe that Extremely Likely (4) is
twice as much belief as Slightly Likely (2). While a scale made up of
many such items will probably exhibit interval properties, this does
not apply to the items themselves.

I am inclined to agree with Ronan. Like I said before, I don't think ordinal regression is all that hard to understand, and as Ronan reiterates assumptions about normally distributed homoskedastic error terms are clearly violated with short ordinal scales.

Having said that, I find this example interesting:

use "http://www.indiana.edu/~jslsoc/stata/spex_data/ordwarm2.dta";, clear
tab1 warm
reg warm  yr89 male white age ed prst
ologit warm  yr89 male white age ed prst, nolog

In this example, the T/Z values are virtually identical across the two methods, and the coefficients are in the same ratios to each other (i.e. in the ologit the coefficients are all about twice as large as they are in the regression).

Of course, this is just one example, and there are other ordinal variables where it is clearly unreasonable to think that the categories are evenly spaced. But this gives hope that nothing too terrible happens if your typical scale ranging from "Strongly Disagree" to "Strongly Agree" is analyzed by ols rather than ordinal regression.

You would think somebody would have done a paper comparing ols to ordinal regression of such items - if so, does anybody have a citation?


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Richard Williams, Notre Dame Dept of Sociology
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