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Re: st: Re: heteroscedasticity in logit/ probit model


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Re: heteroscedasticity in logit/ probit model
Date   Wed, 24 Nov 2010 16:39:18 +0000 (GMT)

--- On Wed, 24/11/10, rohaida wrote:
> Let me clarify my problem. In linear model we use "estat
> imtest" and "estat hettest" command to check heteroscedasticity.
> If heteroscedasticity exist the OLS is inefficient, then we can
> use the GLS (weighted least square) or robust std. error to
> correct heteroscedsaticity. 
> 
> So, how about the probit/logit model? how can I check
> heteroscedsaticity in logit/ probit model? If heteroscedasticity
> exist in the probit/ logit model how can I fix it? This is useful
> to defend which estimator that give unbiased results. What
> actually 'hetprob' function?

Heteroskedasticity is a very different problem in models like -probit- 
and -logit-. Think of it this way: your dependent variable is a 
probability. A probabiltiy embodies uncertainty, and that uncertainty
comes from all variables we have not included in our model. In one
sense this makes it very easy to deal with heteroskedasticity: We just
define our dependent variable of interest to be the probability given
the control variabels in our model. The results of your model give an
accurate description of what you have found in your data. However, we 
often want to give parameters a counterfactual interpretation (e.g. 
"if the men suddenly became women, then the probabiltiy changes by x
percentage points"). Such a counterfactual interpretation is only
correct if we can assume that there is no heteroscedasticity. Several
solutions have been proposed and I trust none of them: they are just
too sensitive. If you really want to do something about it, than I 
you'll really need to do some reading. Since these models are so 
sensitive, you really need to know what you are doing. A good entry
point for that literature is (Williams 2009). But my position is that
that problem is basically unsolvable, so not worth worrying about.

Hope that helps,
Maarten

Williams, R. 2009. Using heterogenous choice models to compare logit 
and probit coefficients across groups. Sociological Methods & Research 
37: 531--559.

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

http://www.maartenbuis.nl
--------------------------


      

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