MATH3091 Statistical Modelling II
Module Overview
The module Statistical Modelling II covers in detail the theory of linear regression models, where explanatory variables are used to explain the variation in a response variable, which is assumed to be normally distributed. However, in many practical situations the data are not appropriate for such analysis. For example, the response variable may be binary, and interest may be focused on assessing the dependence of the probability of 'success' on potential explanatory variables. Such techniques are important in many disciplines such as finance, market research and medicine. Alternatively, a variety of biological and social science data are in the form of cross-classified tables of counts, called contingency tables. The structure of such tables can be examined to determine the pattern of interdependence of the cross-classifying variables.
Aims and Objectives
Module Aims
To cover the theory and application of generalised linear models. This is an extremely broad class of statistical models, which incorporates the linear regression models studied in Statistical Modelling II, but also allows binary or count data to be modelled coherently. A series of flexible estimation and model comparison procedures are introduced and used to analyse appropriate data. The statistical programming language R is used throughout
Learning Outcomes
Learning Outcomes
Having successfully completed this module you will be able to:
- Derive properties of the exponential family and determine whether a given distribution is a member of the exponential family.
- Apply likelihood theory to conduct inference in generalised linear models: estimate parameters, construct confidence intervals, make predictions and compare candidate models.
- Fit appropriate generalised linear models to data using R and interpret the fitted models.
- Interpret log-linear models in terms of independence and conditional independence.
Syllabus
The module consists of 11 weeks of lectures. The topics for the weeks are roughly as follows: Week 1: Introduction. Revision of distribution and motivation for GLM. Week 2-3: Revision of likelihood-based inference and linear models. Weeks 4-8: GLMs: theory and application. Weeks 9-11: Log-Linear models and contingency tables.
Learning and Teaching
Teaching and learning methods
.
| Type | Hours |
|---|---|
| Teaching | 48 |
| Independent Study | 102 |
| Total study time | 150 |
Resources & Reading list
Faraway J. Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models.
Dobson AJ & Barnett AG. An Introduction to Generalized Linear Models.
Cox DR & Snell EJ. Analysis of Binary Data.
Agresti A. An Introduction to Categorical Data Analysis.
McCullagh P & Nelder JA. Generalized Linear Models.
Assessment
Summative
| Method | Percentage contribution |
|---|---|
| Coursework | 20% |
| Exam | 80% |
Referral
| Method | Percentage contribution |
|---|---|
| Exam | 100% |
Repeat Information
Repeat type: Internal & External
Linked modules
Pre-requisites: MATH2010 AND MATH2011
Costs
Costs associated with this module
Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.
In addition to this, students registered for this module typically also have to pay for:
Books and Stationery equipment
Course texts are provided by the library and there are no additional compulsory costs associated with the module
Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.