The Logit Model:

Setting F(x_iβ) to be  the logistic distribution,  in  the  regression approach (used  in many analyses), gives rise to  the  logit model. Similarly,  in  the  latent regression ap  roach, assuming that  E,  follows a  logistic  distribution, with  known  variance (Π²/3),  conditional on  q, will give  rise  to the  logit model. The  logistic distribution function is given by  '.  

An  interesting  property  of the  logistic distribution is  that  its probability density function,

The expressions in  (12.2), (12.14) and (12.16) may be written as,'

dividing both numerator and denominator by e^-x_iβ we  have