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Re: st: hetroscedasticity test after probit

From   Maarten Buis <[email protected]>
To   [email protected]
Subject   Re: st: hetroscedasticity test after probit
Date   Thu, 5 Jul 2012 11:53:53 +0200

On Thu, Jul 5, 2012 at 11:27 AM, Yuval Arbel wrote:
> 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?

Not quite, as we defined the probability in terms of the variables in
our model, so we are by definition not omitting relevant variables.
The problem is that the probability is only defined within the context
of the model. A probability is a measure of uncertainty. This does not
mean that uncertainty is "unexplainable", we can always find
"explanations" for random events and put those "explanations" into
variables. However, (hopefully) for substantive reasons we have
classified these variables as random/unsystematic. (*) Once we have
made our choice there is, by definition, no omitted variable problem,
but the difference in variance of the omitted/random/unsystematic
variables across included co-variates will still cause problems if we
wish to interpret our results in a causal/counter-factual way.

Another way to think about this is to consider what would happen if we
could control for everything. In that case there is no uncertainty
left and the "probabilities" would be either 0 or 1 for all
observations and the (linear additive) effects could only be -1, 0, or
1. This is typically not the kind of estimate of interest.

Hope this helps,

(*) In practice we typically we do so by omission: we choose a set of
variables to include in our model and define everything else as

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