This test is to be written in the BSB Student Technology Centre. The duration of the test is 2 hours.
Any aids and resources are permitted. You may consult any web pages but you may not use e-mail or communicate with anyone other than the instructor.
Part A.
Question 1.
Consider linear Poisson regression through the origin, mu = beta*x. Find the log-likelihood, score and information for beta. Pick some x-values and generate data from this model. Plot your data. Use scoring to fit the data and find 95% confidence intervals for beta by the likelihood-ratio, score and Wald methods. Compare your results with
summary(glm(y ~ x - 1, family = poisson(link = identity)))
Question 2.
Consider log-linear Poisson regression through the origin, log(mu) = beta*x. Find the log-likelihood, score and information for beta. Pick some x-values and generate data from this model. Plot your data. Use scoring to fit the data and find 95% confidence intervals for beta by the likelihood-ratio, score and Wald methods. Compare your results with
summary(glm(y ~ x - 1, family = poisson(link = log)))
Part B.
The numbered problems are from Agresti, A. (2002), Categorical Data Analysis, Wiley.
Chapter 2
2.3, 2.8