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Re: st: Heteroskedastic Probit Model

From   Maarten buis <>
Subject   Re: st: Heteroskedastic Probit Model
Date   Thu, 22 Apr 2010 12:51:59 -0700 (PDT)

--- On Thu, 22/4/10, Richard Williams wrote:
> True, but if you just throw up your hands and say you will
> assume no hetero, that has problems too.  You may get
> estimates that are misleading, particularly if, say, you are
> interested in things like group comparisons of
> effects.  If you have a theoretically plausible model,
> you can test whether the variables in the variance equation
> have significant effects.  Alas, if the model is wrong
> that can also lead to incorrect conclusions.  But
> you're taking a risk whatever you do, so you should think
> about what makes most sense while realizing that other
> things may make sense too.

The issue is that you have to be clear where the information
is comming from you present the conclusions.  Normally, our 
conclusions receive their credibility from the fact that 
they summarize what we have seen.  However, with these
models a really substantial part of that information comes 
from assumptions that are either very hard or impossible to
check.  So you need to give some other reason why we should
believe the results, which is usually a theory that states
that a certain variable influences the residual variance in 
a certain way.  This precludes a kitchen-sink model.  

Also, these models require that every part of the model is 
correct, not only the functional form of the residual 
variance equation, but also the functional form of every
control variable in the main equation (getting the main
equation wrong works through in the residuals, and the 
residual part of the model works back again on the main
part).  So using such a model requires some very rigorous 
sensitivity analysis.  

Hope this isn't too depressing,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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