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

[Richard Williams <Richard.A.Williams.5@ND.edu>]

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.


-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
FAX:    (574)288-4373
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
WWW (personal):    http://www.nd.edu/~rwilliam
WWW (department):    http://www.nd.edu/~soc 
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/