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RE: st: Likelihood function of uniform distribution

From   "Verkuilen, Jay" <>
To   <>
Subject   RE: st: Likelihood function of uniform distribution
Date   Wed, 2 Apr 2008 18:38:37 -0400

Mostafa Beshkar wrote:

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


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


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

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 explains things quite

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. :) 


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