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Re: st: hetroscedasticity test after probit

From   Yuval Arbel <>
Subject   Re: st: hetroscedasticity test after probit
Date   Thu, 5 Jul 2012 12:27:33 +0300

Maarten, I believe your implication refers to specification errors in
the model, i.e., omission of relevant explanatory variables, leading
to biased and inconsistent estimates and predictions. Am I correct?

On Thu, Jul 5, 2012 at 11:56 AM, Maarten Buis <> wrote:
> On Thu, Jul 5, 2012 at 10:32 AM, Yuval Arbel wrote:
>> Prakash, returning to your original question, I see no point at all to
>> check for hetroscedasticity after -probit- simply because this problem
>> is inherent in the family of models with binary dependent variables.
>> Take, for example, the so called LPM (linear probability model), where
>> the dependent variable is derived from Binomial distribution (which
>> is by itself an approximation to the Normal distribution, from which
>> the probit model is derived). Every elementary Econometric textbook
>> (e.g. Jan Kmenta, Elements of Econometrics, 1997, pp. 548-549), will
>> show you a very simple proof revealing the fact that the LPM is
>> inherently heteroscdastic, where the variance of the random
>> disturbance term equals yhat(1-yhat) and yhat is the vector of
>> predicted values
> The problem is subtly but completely different with models like
> -probit- and -logit-. These models already use the variance function
> yhat(1-yhat), so there is no need to further adjust for that.
> However, heteroskedasticity is still a huge and unsolvable problem in
> these models. 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
> --------------------------
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Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street,
Haifa 33031, Israel
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