9 1 Let Y1 Yn Be Independent Random Variables With Y Po Ui And Log M B1 2 Xijssj I 1 N A Sho 1 (48.82 KiB) Viewed 27 times
= 9.1 Let Y1, ... ,Yn be independent random variables with Y; . Po(ui) and log M; = B1 +£';=2_xijßj, i = 1,...,N. a. Show that the score statistic for B1 is Un = {{_1(Y; – Mi). b. Hence, show that for maximum likelihood estimates Ûi, Elli = £yi. c. Deduce that the expression for the deviance in (9.6) simplifies to (9.7) in this case. N =
The deviance for a Poisson model is given in Section 5.6.3. It can be written in the form D=2 [0; log(0;le;) – (0; – ei)]. (9.6) However, for most models L0; = Lei (see Exercise 9.1), so the deviance simplifies to D=2 [0;log(0i/e;)]. (9.7) =
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