STATISTICS 4C03/6C03
Special Instructions:
This exam consists of THREE questions.
This exam is to be written in the BSB Computer Lab. You must have a paid-up printing account in the lab.
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.
Data sets for Questions 1 & 2 are taken from Agresti, A. (1996) An Introduction to Categorical data Analysis, Wiley.
Analyze the multi-way contingency table from Problem 8.20 on p. 225 of Agresti.
Use a Poisson loglinear model to analyze the data from Table 4.2 on pp. 82-83 of Agresti, available as file crabsat.txt. Each female crab in the study had a male crab attached to her in her nest. The study investigated factors that affect whether the female crab had any other males, called satellites, residing nearby her. The variables are:
color (1 = light medium, 2 = medium, 3 = dark medium, 4 = dark)
spine (1 = both good, 2 = one worn or broken, 3 = both worn or broken)
width = carapace width (cm)
sat = number of satellites
weight = weight (kg)
Consider the data in the file q3.txt. The error distribution is normal.
Choose a suitable link function by finding a transformation of the y-axis that makes the relationship a straight line.
Choose a suitable variance function by computing the sample mean and variance for the y values at each distinct x value and plotting variance against mean.
Fit this model to the data by Maximum Likelihood and by Maximum Quasi-Likelihood and compare the results. Compute the relative efficiency of the two methods.