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Re: st: predict options in heckprob

From   [email protected] (Roberto G. Gutierrez, StataCorp.)
To   [email protected]
Subject   Re: st: predict options in heckprob
Date   Mon, 19 Aug 2002 16:20:47 -0500

Alan Feiveson <[email protected]> asks:

> Hello - I notice in the writeup for heckprob under "Options for predict"
> (Stata 7 manual H-P, p.33), "p10" is defined as the predicted joint
> probability that y(probit)=1 and y(select)=0. I thought that under this
> model, y(probit) is only observed if y(select)=1. Therefore the joint
> probability should be zero.

> Concerned about this, I tried -heckprob- on the example on pp. 36-7 with
> (1): y(probit) as originally constructed in the example (i.e. all 0's and
> 1's, no missing) and (2): y(probit) set to missing when y(select)=0.

> I was relieved to see that I got the same estimation results whether or not
> y(probit) was set to missing or zero when y(select)=0. Using the "p10"
> option, however, I obtained non-zero values. Apparently, what is calculated
> is the joint probability of y1*>0 and y2* >0 where y1* and y2* are the
> underlying latent normally distributed variables for y(probit) and
> y(select). While I agree that P(y1*>0 , y2* < 0) may be of some interest,
> the writeup should be changed to reflect what is really being calculated.

y(probit) and the event "y1*>0" are one in the same, they either both 
evaluate to true (1) or false (0).  Therefore P{y(probit)==1} and 
P(y1*>0) are equal.  

However, there are situations where y(probit) is left unobserved (when
y(select)=0), but that doesn't change the fact that the (unobserved) value
exists somewhere out there and is equal to 0 or 1.  To see this, think about
performing the following experiment:  flip a fair coin and walk away while the
coin is still in the air.  I contend that the probability of flipping a head
is 0.5 even though you were never around to see it.

As such, I think the terminology in the manual is correct as it stands.

[email protected]
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