Question: Let y i , i = 1,...,n, denote n independent binary random variables. a. Derive the log likelihood for the probit model Φ 1 [Ï(x

Let yi, i = 1,...,n, denote n independent binary random variables.

a. Derive the log likelihood for the probit model Φ€“1 [Ï€(xi)] = ˆ‘j βj xij.

b. Show that the likelihood equations for the logistic and probit regression models are

E(y – â,) z,xij = 0, j = 0,..., p,


where zi = 1 for the logistic case and zi = Ï•(ˆ‘j β̂j xij)/π̂i(1 €“ π̂i) for the probit case.

E(y ,) z,xij = 0, j = 0,..., p,

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