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Re: st: Predicted probabilities after oprobit w/robust standard errors


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Predicted probabilities after oprobit w/robust standard errors
Date   Fri, 02 Jun 2006 08:14:48 -0500

At 06:55 PM 6/1/2006, Matt Barmack wrote:
Specifying cluster or robust does not seem to change the predicted
probabilities from oprobit.  Does it?  Shouldn't it?
Intuitively/naively, I am thinking that for an observation for which
the variance of the random part of the latent index is high, there is
a greater chance of ending up further away from what the
deterministic part of the latent index alone might suggest.
Interesting point about the intuition, but it is not right in this case. The predict command does allow you to also estimate the standard error of the linear prediction, which I think gets at the issue you are raising, and the standard error of the prediction is affected by whether or not you use cluster or robust.

As to why your intuition is wrong - well, if it were correct, it would mean that you would, say, with higher standard errors, be more likely to predict that every case was a 5 or a 1 on a 5 pt scale. Why should that be the case, i.e. why should higher standard errors make it more likely that cases have extreme values? The predictions are not affected by the standard errors in this way, but our confidence in how accurate the predictions are is.

Also, in probit, the residual is assumed to have a normal(0, 1) distribution. That is true regardless of what the standard errors are. Together, the linear prediction, the cutpoints, and the distribution of the residual will determine what the predicted probabilities are.


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Richard Williams, Notre Dame Dept of Sociology
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