The data in Table 4.5 of (Dobson and Barnett 2018) show the numbers of cases of AIDS in Australia by date of diagnosis for successive 3-month periods from 1984 to 1988. (Data from National Centre for HIV Epidemiology and Clinical Research, 1994.) In this early phase of the epidemic, the numbers of cases seemed to be increasing exponentially. a. Plot the number of cases yi
3. The data in Table 4.5 of (Dobson and Barnett 2018) show the numbers of cases of AIDS in Australia
by date of diagnosis for successive 3-month periods from 1984 to 1988. (Data from National Centre for
HIV Epidemiology and Clinical Research, 1994.) In this early phase of the epidemic, the numbers of
cases seemed to be increasing exponentially.
a. Plot the number of cases yi against time period i, i = 1, . . . , 20).
b. A possible model is the Poisson distribution with parameter λi = i
θ
, or equivalently
ln λi = θi
ln i.
Plot ln yi against ln i to examine this model.
c. Fit a generalized linear model to these data using the Poisson distribution, the log-link
the equation
g(λi) = ln λi = β1 + β2xi
,
where xi = ln i.
10
Firstly, do this from first principles, using Fisher’s scoring and using software which can perform matrix
operations to carry out the calculations.
Find the Score function, the estimating equation and the information matrix.
d. Fit the model described in (c) using statistical software which can perform Poisson regression. Compare
the results with those obtained in (c).
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
