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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 * * 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/ * * 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:*Maarten buis <maartenbuis@yahoo.co.uk>

**RE: st: Likelihood function of uniform distribution***From:*"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>

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

**RE: st: Likelihood function of uniform distribution***From:*"Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>

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