Re: st: St: Ordered Logit Question

[Richard Williams <Richard.A.Williams.5@ND.edu>]

At 06:15 PM 5/6/2009, Jason Dean, Mr wrote:
> I am running two ordered logits equations. One for immigrants and 
> one for the native-born. Each has the exact same independent and 
> dependent variables. There are 3 categories for the depedent 
> variable. I find that the threshhold parameters are quite different 
> for these two groups. Specifically, both cutpoints are much lower 
> for immigrants. Can anyone enlighten me as to how I should interpret 
> this? To me this means, all else equal, immigrants are much more 
> likely to be in the highest category and much less likely to be in 
> the lowest category. Can I just interpret this in a similar manor as 
> if these two groups had different intercepts in a linear regression? 
> Also, is it appropriate to compare marginal effects between 
> immigrants and the native-born.
>
> Any help would be greatly appreciated.

In general, I don't recommend eyeball comparisons of separate models 
estimated on different populations, and I especially don't recommend 
it with techniques like ordinal regression.  Without going into all 
the gory details, it can have much the same problems that comparing 
standardized coefficients across populations does.  (If you do want 
the gory details, see 
http://www.nd.edu/~rwilliam/oglm/RW_Hetero_Choice.pdf and/or 
http://www.nd.edu/~rwilliam/oglm/oglm_Stata.pdf ).

Suppose you follow Clive's advice and estimate a pooled model with a 
dummy variable for group membership, and suppose the coefficient for 
that dummy is significant and positive.  The usual interpretation is 
that, when all other things are equal, members of one group tend to 
score higher on your dependent variable than do members of the other group.

The more annoying possibility, that you may at least want to 
consider, is that there is "index shift", i.e. people are using 
different criteria when responding to the question.  So, for example, 
suppose the question has to do with pain and the options are "Lot of 
pain, moderate pain, little or no pain."  A man and a woman might 
feel the same amount of pain; but if men tend to be big babies, a man 
might say he has a lot of pain while a woman with the same amount of 
pain would only say it was moderate.

Or, suppose the DV has something to do with accomplishments or 
abilities.  If one culture tends to be more modest than the other, it 
might tend to report lower values on the ordinal DV than the other 
does even if the level of accomplishments/abilities is identical.

Put another way, there is always the question of whether observed 
differences are real or whether they are artifacts of group 
differences in measurement.  Cross-group differences in measurement 
are going to be problematic in any analysis; but they may be 
especially problematic with an ordinal DV.  With an ordinal DV, you 
are usually (or at least often) thinking that it is a collapsed 
version of some underlying continuous DV, e.g. pain falls along a 
continuum, it doesn't have just 3 values.  The problem is that people 
decide for themselves how the collapsing should be done, and there is 
nothing that says all members of all groups are going to do it the same way.

I must say that, the more I learn about categorical data analysis, 
the more I think you should kill to try to get variables that work in 
an OLS-type framework...  :)


-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
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