Consider the general log-likelihood function given in (13.16). Assume that all the regression slopes are zero except for the constant . (a) Show that maximizing

Consider the general log-likelihood function given in (13.16). Assume that all the regression slopes are zero except for the constant α.

(a) Show that maximizing log with respect to the constant α yields  F(α) = ¯y, where ¯y is the proportion of the sample with yi = 1.

(b) Conclude that the value of the maximized likelihood is logr = n[¯ylog¯y + (1 − ¯y)log(1 − ¯y)].

(c) Verify that for the union participation example in section 13.9 that logr = −390.918.