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Re: st: hetroscedasticity test after probit


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: hetroscedasticity test after probit
Date   Thu, 5 Jul 2012 14:02:07 +0200

On Thu, Jul 5, 2012 at 1:33 PM, Prakash Singh wrote:
> I just saw this paper (Parikh ans Sen 2006, Applied Economics Letters
> 2006, 13, 699-707) where they have tested the presence of
> hetroscedasticity both in probit and hetpro estimators.
>
> Though, I agree with Maarten but I wanted to do this test as the
> referee has asked me perform so if there is any way I can test it.

I would not test for it, as you just cannot test for it. This type of
heteroscedasticity does not refer to residuals we can see, that is the
observed - predicted values but to a difference between two unobserved
quantities: the latent and predicted value.

The information that is used to estimated such heteroscedastic probit
models is typically a deviation from "linearity"(*) in the effects of
the observed variables (e.g.
<http://www.maartenbuis.nl/wp/uh_logistic.html>). Now linearity is
almost always nothing but a convenient simplification of reality and
is not believed to be strictly true. These models, however, cannot
distinguish between the to be expected small deviations from linearity
and heteroscedasticity. As a consequence these models are just way to
fragile. You may get completely different estimates with them, but
that tells you exactly nothing.

I would just frame the results as descriptive, as that is true and
regardless of the presence or absence of heteroscedastictiy. The trick
is to explain your results in terms of comparing groups, i.e. the
probability of success in group 1 can be a and in group 2 b, so the
groups differ in probability by b - a. However, this does not mean
that the probability of success of persons in group 1 would change by
b - a when they changed to group 2, because they will take the
residual variance of group 1 with them.

Hope this helps,
Maarten

(*) within the linear predictor not with respect to the predicted probability.

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


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