The University of Southampton
Courses

# MATH3012 Statistical Methods II

## Module Overview

The module Statistical Methods I 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 Methods I, 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 interactive statistical computer language R or S-Plus is used throughout

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• Recall the definition of a generalised linear model;
• Analyse binary and binomial data using logistic regression models, and other generalised linear models where appropriate
• Estimate coefficients of a generalised linear model using maximum likelihood, interpret the estimates and calculate confidence intervals for the estimates
• Interpret log-linear models in terms of independence and conditional independence
• Compare generalised linear models using likelihood ratio tests
• Use exponential family and likelihood theory to derive important results for generalised linear models
• Assess goodness of fit of a generalised linear model using deviance and residuals
• Analyse data appropriately using R or S-Plus
• Use generalised linear models to evaluate predictions and assess the corresponding uncertainty

### 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/linear models. Weeks 4-8: GLMs: theory and application. Weeks 9-11: Log-Linear models and contingency tables. Likelihood based statistical theory will also be introduced as and when required

### Learning and Teaching

TypeHours
Independent Study102
Teaching48
Total study time150

#### Resources & Reading list

Krause A & Olson M. The Basics of S and S-PLUS.

Cox DR & Snell EJ. Analysis of Binary Data.

Krzanowski W. An Introduction to Statistical Modelling.

Collett D. Modelling Binary Data.

Dobson AJ. An Introduction to Generalized Linear Models.

Venables WN & Ripley BD. Modern Applied Statistics with S.

McCullagh P & Nelder JA. Generalized Linear Models.

Agresti A (2007). An Introduction to Categorical Data Analysis.

### Assessment

#### Summative

MethodPercentage contribution
Coursework 20%
Exam 80%

#### Referral

MethodPercentage contribution
Exam 100%

#### Pre-requisites

To study this module, you will need to have studied the following module(s):

CodeModule
MATH2011Statistical Distribution Theory
MATH2010Statistical Methods I

### 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.