Transcription of The Logit Model: Estimation, Testing and Interpretation
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The Logit Model: estimation , Testing and InterpretationHerman J. BierensOctober 25, 20081 Introduction to maximum likelihood The likelihood functionConsider a random sampleY1, .., Ynfrom the Bernoulli distribution:Pr[Yj=1]=p0Pr[Yj=0]=1 p0,wherep0is unknown. For example, tossntimes a coin for which you suspectthat it is unfair:p06= ,and for each tossingjassignYj=1if the outcomeis heads andYj=0if the outcome is tails. The question is how to estimatep0and how to test the null hypothesis that the coin is fair:p0= probability function involved can be written asf(y|p0)=Pr[Yj=y]=py0(1 p0)1 y=(p0ify=1,1 p0ify= , lety1, .., ynbe a given sequence of zeros and ones. Thus, eachyjis ei-ther0or1. The joint probability function of the random sampleY1,Y2.)
The idea of maximum likelihood (ML) estimation is now to choose p such that L n(p) is maximal. In other words, choose p such that the probability of drawing this particular sample Y1,...,Y n is maximal. ... is the distribution function of the logistic (Logit) distribution.
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