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Re: st: Heteroskedastic Probit Model

From   Maarten buis <>
Subject   Re: st: Heteroskedastic Probit Model
Date   Thu, 22 Apr 2010 12:43:59 +0000 (GMT)

--- On Thu, 22/4/10, Mustafa Brahim wrote:
> you mentioned that "most of the information is comming
> from your assumptions (primarily functional form assumptions)"
> and you conclude that I do not have a good theoretical
> background.

I am not doubting your skills or knowledge concerning theory,
I only stated that the information used to estimate this model
comes mostly from a very specific theory concerning the 
functional form of the relationship between the residual 
variance and some explanatory variables, rather than from the 
data, and that your question indicated that you did not have 
that particular theory. This is not a personal attack, this 
theory probably does not exist for most applications.

> So because no one tested the model for heteroskedasticity
> does not mean that I should not test mine. You suggested
> not to use hetprob,the question then is  how am I going
> to check whether it exists or not?

In the end the purpose of a test (or any statistical modeling)
is to extract information from the data, so the first step
would be figure out whether such information is even present
in the data. My argument was that there is so little 
information on this issue available in the data, that this test 
only makes sense in very specific situations where you have 
very specific theories that can help you identify the model. 

To be concrete: Heteroskedasticity represents a change in the 
variance of the residual. The residual is the difference 
between the observed and expected value in your model. In the 
probit model the "observed" value isn't observed but latent, 
i.e. not directly observed. So, this model uses the expected 
value, which is not directly observed (it is a function 
of your model), the "observed" value, which is not 
observed (it is latent), it computes a difference between
these unobserved things, and than looks at how the 
variance of this doubly unobserved thing changes over some 

To quote John Tukey (1986), "Sunset salvo". The American
Statistician 40(1): "The combination of some data and an 
aching desire for an answer does not ensure that a reasonable 
answer can be extracted from a given body of data." 

Hope this helps,

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


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