Logit and Probit Notes - Lecture Notes On Binary Choice Models Logit and Probit Thomas B Fomby Department of Economic SMU March 2010 Maximum Likelihood

# Logit and Probit Notes - Lecture Notes On Binary Choice...

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Lecture Notes On Binary Choice Models: Logit and Probit Thomas B. Fomby Department of Economic SMU March, 2010 Maximum Likelihood Estimation of Logit and Probit Models i i i P P y - 1 y probabilit with 0 y probabilit with 1 Consequently, if N observations are available, then the likelihood function is N i y i y i i i P P L 1 1 1 . (1) The logit or probit model arises when i P is specified to be given by the logistic or normal cumulative distribution function evaluated at i X . Let i X F denote either of theses cumulative distribution functions. Then, the likelihood function of both models is N i y i y i i i X F X F L 1 1 1 . (2) Then, the log-likelihood function is N i i i i i X F y X F y l L 1 1 ln 1 ln ln . (3) Now, the first order conditions arising from equation (3) are nonlinear and non-analytic. Therefore, we have to obtain the ML estimates using numerical optimization methods, eg, the Newton-Raphson method.

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