CATEGORICAL DATA ANALYSIS - F73SJ2 - SPRING 2005

• to develop students' abilities in understanding and solving practical statistical problems involving categorical data
• to present theory and techniques for the analysis of categorical data
• to enable students to learn how to choose appropriate techniques, to analyse categorical data, and present results

• recognise data as being categorical data and summarise data as categorical data where appropriate
• appreciate the methods available for the analysis of such data and distinguish between methods which are appropriate and those which are not
• demonstrate skills in using standard analytic methods for single and two-way classification data, including the use of Poisson and multinomial models for data, odds ratios, and Pearson's chi-squared and likelihood ratio statistics
• appreciate the need for, the structure, and the usefulness of, generalised linear models
• fit, and interpret the results of fitting, generalised linear models, including log-linear models (for example trend models) and logistic regression models
• select and fit good models in three-way situations using a formal hierarchical approach

The module is based on two workbooks, which will be given out to all students and which contain necessary background and theory, data sets, and worked examples. There will be 3 lectures per week - the emphasis will be on your learning at your own pace and in your chosen manner rather than every detail being taught. In lectures we will consider the main points from the theory and applications described in the workbooks and we will go over the worked illustrations and examples.

Practical applications will be emphasised throughout - most of the practical work will be done on computer using R (and very occasionally Minitab).

Note that you will be expected to learn some of the material for yourself both from studying the content of the workbooks and from doing the practical work contained in the tutorials. Not every part of the work will be taught as such.

Each student will be expected to attend one computer lab (at which RJG will be present) in week 2, week 4 or 5 (or both), week 7, and week 9. These will be held at 12.15hrs and 14.15hrs in the main lab on the ground floor of the Scott Russell building. In addition labs are reserved for students taking this module at other times (see the timetable on the door of the lab).

TIMETABLE

Class times - including lectures, tutorials, and worked examples sessions (using R):
Weeks 1 - 4 and 6 - 9 Tuesday 14.15, Wednesday 09.15, 10.15
There are no lectures in weeks 5 or 10.

Labs (SR G13): Weeks 2,4,5,7,9
Monday 12.15, 14.15
The labs in Weeks 4,5 and 9 will be special "Project labs".

CONTENT

1. Introduction
2. Poisson process and associated distributions
   1. Bernoulli trials and related distributions
   2. Poisson process and related distributions
   3. Inference for the Poisson distribution
   4. Dispersion and likelihood ratio tests for Poisson data
   5. Mixed and compound Poisson distributions
3. Single classifications
   1. Binary classifications
   2. Qualitative categories
   3. Ordered categories
   4. Goodness-of-fit tests for frequency distributions
   5. Residuals
   6. Trend models
   7. Cyclic models
   8. A brief introduction to generalised linear models
4. Two-way classifications
   1. Factors and responses
   2. Distribution theory for 2x2 tables
   3. Statistical tests for 2x2 tables
   4. The odds ratio for a 2x2 table
   5. Log-linear models for 2x2 tables
   6. rxs tables
   7. Some other situations and special cases
   8. Taking into account a "deterministic denominator" - using an offset
5. Logistic regression
6. Three-way classifications
   1. Introduction
   2. Hierarchic log-linear models