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From |
"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu> |

To |
<statalist@hsphsun2.harvard.edu> |

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. 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 * * 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/

**Follow-Ups**:**RE: st: Likelihood function of uniform distribution***From:*"Mostafa Beshkar" <mostafa.beshkar@vanderbilt.edu>

**References**:**RE: st: Likelihood function of uniform distribution***From:*"Mostafa Beshkar" <mostafa.beshkar@vanderbilt.edu>

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