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RE: st: Differences in regression slopes


From   "Mustillo, Sarah A" <smustill@purdue.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Differences in regression slopes
Date   Wed, 20 Feb 2008 17:53:52 -0500

I've been waiting for you to weigh in on this conversation today!

It really is hard to know the best thing to do, isn't it?

I've been going through both your gologit2 paper and your oglm paper
this week for my own work and I become more convinced each time I read
the oglm paper that you are right about Allison's solution and that the
hetero choice model is superior.  That said, none of these solutions are
ideal!  Perhaps that fact will keep all of us in business for a long
time...

Sarah

Sarah A. Mustillo, Ph.D 
Associate Professor of Sociology
Faculty Associate, Center on Aging and the Life Course
Purdue University
700 W. State St.
West Lafayette IN 47907-2059

765-496-2226

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Richard
Williams
Sent: Wednesday, February 20, 2008 5:46 PM
To: statalist@hsphsun2.harvard.edu; statalist@hsphsun2.harvard.edu
Subject: Re: st: Differences in regression slopes

At 01:11 PM 2/20/2008, Maarten buis wrote:
>The heterogeneous choice model seems to me a very fragile model: you
>estimate a model for both the effect of the observed variables and the
>errors, and you use your model for the errors to correct the effects of
>the observed variables. Any fault in your model will mean the errors
>are off, leading to faults in your model for those errors, which in
>turn will feed back into the estimates of all other parameters.
>
>The simulation below shows this: if the model is correct you will
>reproduce the correct estimates. However, if you misspecify one of the
>effects, all estimates are off, and are actually worse than a normal
>logit.

Maarten makes some very good points here.  In my paper on hetero 
choice models that has been previously cited, I also run simulations 
that show how a mis-specified model can produce very misleading 
results.  Also, even when the model is correctly specified, analysis 
with a dichotomous DV can be problematic.  The paper argues that a 
well-specified model with an ordinal DV can work pretty well, but 
still notes various cautions to be aware of.

Also, Maarten kindly got his comments to me before I made the 
presentation he refers to, which gave me the idea of adding that 
hetero choice models might just be run as a diagnostic technique.  If 
the model indicates that hetero is a problem, rather than use a 
hetero choice model (with the potential problems that Maarten notes) 
you may instead try to find other ways to deal with the hetero, e.g.
take logs.

My own self-assessment of the work is (a) Allison had a very good 
description of the problem (b) my paper has a very good discussion of 
why Allison's proposed solution is flawed, sometimes seriously so (c) 
my proposed solution is better than Allison's in several ways, but 
when and whether it is the best way to go is still open to debate.


-------------------------------------------
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
WWW:    http://www.nd.edu/~rwilliam

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