Rachel <[email protected]> asks,
> My question is why oprobit identifies /cut1 at all, rather than
> normalizing it to zero as certain other statistical packages (such as
> Limdep) do. My understanding is that the ordered probit/logit is
> identified by the relative lengths of the intervals--the cutpoints
> themselves have no meaning. And since the length of the interval
> between infinity and the first cutpoint is always infinite, why is
> this first cutpoint identified at all?
I have two answers:
1. Note that the number of cutpoints is k-1, where k is the
number of outcomes. Perhaps Rachel is thinking k.
2. Even if Rachael is thinking k-1, one can write the ordered
probit model with an intercept. If one does that, then
only k-2 cut points are identified.
An easy way to understand -oprobit- is to use it to fit a standard
(two outcome) probit model. Try the following,
. sysuse auto, clear
. probit foreign mpg
[...]
-------------------------------------- [...]
foreign | Coef. Std. Err. [...]
-------------+------------------------ [...]
mpg | .0960601 .0301523 [...]
_cons | -2.635268 .6841458 [...]
-------------------------------------- [...]
. oprobit foreign mpg
[...]
-------------------------------------- [...]
foreign | Coef. Std. Err. [...]
-------------+------------------------ [...]
mpg | .0960601 .0301523 [...]
-------------+------------------------ [...]
/cut1 | 2.635268 .6841458 [...]
-------------------------------------- [...]
The first thing to note is one intercept (probit), one cut point (oprobit),
which is to say, the single cut point reported by -oprobit- corresponds
to the intercept reported by -probit-.
Next to note is that the intercept and the cut point have different signs.
That, however, is due to interpretation. In probit, the result is
to be interpreted as
Pr(foreign) = Pr(.096*mpg - 2.635 + u > 0)
where u is N(0,1). In oprobit, the result is to be interpreted as
Pr(foreign) = Pr(.096*mpg + u > 2.635)
Thus, the two results mean the same thing. -probit- and -oprobit- fitted the
same model, just as they should.
-- Bill
[email protected]
*
* 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/
