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Re: st: Differences in regression slopes

From   Richard Williams <>
Subject   Re: st: Differences in regression slopes
Date   Wed, 20 Feb 2008 17:46:07 -0500

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
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

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