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RE: st: Likelihood function of uniform distribution


From   "Mostafa Beshkar" <mostafa.beshkar@vanderbilt.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Likelihood function of uniform distribution
Date   Thu, 3 Apr 2008 11:06:38 -0500

Thank you for the citations. As Jay mentioned, my problem is an ordinary
binary regression model. In case of probit, for example, you need to use the
Normal distribution function to define your likelihood evaluator. Since the
normal distribution function is already defined in Stata you can simply use
it in your likelihood evaluator.

In my case, however, the difficulty is that I don't know how to define the
necessary distribution function, i.e., the uniform distribution function.
More specifically, I need to first define the following function:

f(p)=1 if 0<p<1
    =0 otherwise.

Simply, my question is how one can define the above function (or other
functions such as a triangular pdf) in Stata. 

Many thanks,
-----------------------------------------------------------------
Mostafa Beshkar
www.people.vanderbilt.edu/~mostafa.beshkar
SSRN page: http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=418146

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Verkuilen, Jay
Sent: Wednesday, April 02, 2008 5:39 PM
To: statalist@hsphsun2.harvard.edu
Subject: RE: st: Likelihood function of uniform distribution

Mostafa Beshkar wrote:


>>I think I should explain my question in more detail, since I think
there has been some misunderstanding.

Indeed.


>>I want to estimate the following probability model (this comes from my
game-theoretic model):

Pr(s=1|X)=Pr(p>BX)
Pr(s=0|X)=1-Pr(p>BX)

where s is a binary variable, X is the vector of observable variables, B
is the vector of parameters to be estimated, and p is an unobservable
random varibale that is distributed according to F on the interval
[0,1].<<

Unless I'm mistaken, this is just an ordinary binary regression. You
actually observe S = 0 or 1, you have a vector of predictors for
characteristics of each choice. The usual random utility formulation
sets BX on the real line and uses a link function generated by making
assumptions about the distribution of the disturbance in a random
utility model. Kenneth Train's most excellent book on discrete choice
(see http://elsa.berkeley.edu/books/choice2.html) explains things quite
well. 

Depending on your design, you will have dependency among observations
because you have observed choices for two players in the same game, you
are in a more complex situation requiring simultaneous equations with a
non-recursive model. There is a literature on econometrics in the
context of game theoretic models; I am aware of it but don't know much
about what's going on currently. I'm guessing that biprobit in Stata
(generalizes probit to two simultaneous equations) would be of help.
Googling and a trip to Jstor gives: Estimation of Econometric Models of
Some Discrete Games, Peter Kooreman,  Journal of Applied Econometrics,
Vol. 9, No. 3. (Jul. - Sep., 1994), pp. 255-268. 

I must confess this is getting out of my area.... I is just a poor, dumb
psychometrician. :) 

Jay

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