Consider the linear logit model (5.5) for an I ×2 table, with yi a bin( n i ,π i )variate. a. Show that the log likelihood is b. Show that the sufficient statistic for β is ∑ i y i x i , and explain...

Consider the linear logit model (5.5) for anI×2 table, withyia bin(n_i
,π
_i
)variate.

a.Show that the log likelihood is

b.Show that the sufficient statistic for β is ∑
_i y_i x_i
, and explain why this is essentially the variable utilized in the Cochran-Armitage test.(Hence that test is a score test ofH
₀: π =0).

c.LettingS=∑
_i yi, show that the likelihood equations are

d. Let. Explain whyand

Explain why this implies that the mean score onxacross the rows in the first column is the same for the model fit as for the observed data. They are also identical for the second column.