The University of Southampton
Courses

# STAT6083 Generalised Linear Models

## Module Overview

To introduce the theory of GLMs and apply the models in practice. The module is divided in 5 sections as explained below: Section 1. Introduction: Review of statistical modelling, Linear Regression, Deviance, model checking and regression diagnostics. Section 2. Foundations of GLMs: Foundations of Generalised Linear Models, the exponential family of distributions and its properties, Maximum Likelihood estimation, Score functions and Information, the Newton-Raphson and Fisher scoring algorithms. Section 3. Categorical data and Logistic regression (Binary/Multinomial/Ordinal): One-way contingency tables, two-way contingency tables, measures of association, odds ratios and properties of odds ratios. Binary logistic regression, probit regression, multinomial logistic regression, ordinal logistic regression, Maximum Likelihood Estimation, latent variable approach, deviance, residual analysis and model selection. Section 4. Poisson regression and log-linear models: Models for count data / Poisson regression, Log-linear models for rates, offset terms. Over dispersion and Negative-Binomial regression. Log-linear models for multi-way contingency tables and Simpson’s paradox. Residual analysis, Model selection, Deviance and Likelihood Ratio tests. Section 5. Advanced topics: Robust regression, data driven transformations, Non-parametric regression, kernel, and spline models. Pre-requisite for STAT6079 One of the pre-requisites for STAT6108

### Aims and Objectives

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• Summarise data with an appropriate statistical model.
• Use models to describe the relationship between a response and a set of explanatory variables.
• Interpret the results of the modelling.
• Use the statistical software package R to fit statistical models.
• Understand the foundation theory of Generalised Linear Models.
• Use a range of popular statistical models for continuous and categorical data.

### Syllabus

Overview of statistical modelling, linear regression models, one-way contingency tables, quantilequantile plots, two-way contingency tables, log-linear models for rates, dummy variables and interactions, model selection, log-linear models for multi-way contingency tables, logistic regression models, regression diagnostics, multinomial logistic regression models, models for ordinal data, exponential family of distributions, Poisson regression, Negative-binomial regression, non-parametric regression, robust fitting methods, Median regression and M-estimation.

### Learning and Teaching

#### Teaching and learning methods

Teaching will be through a combination of lectures, and computer workshops. Learning activities will include learning in lectures, which will cover explanations of the statistical modelling techniques and their use, as well as by independent study. The computer workshops will provide hands-on experience of the analysis of data and the application of the techniques introduced in the lectures, enabling you to undertake the statistical computing element of the coursework assignment.

TypeHours
Teaching40
Independent Study160
Total study time200

Dobson, A. J. (2008). An Introduction to Generalized Linear Models.

On-line resources. There will be a blackboard site where all the module materials (slides, computer worksheets, assignments, list of books, etc.) will be made available.

Fox, J. (1997). Applied Regression Analysis, Linear Models, and Related Methods.

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

Agresti, A. (2002). Categorical Data Analysis.

Fox, J. (2002). An R and S-PLUS Companion to Applied Regression.

### Assessment

#### Summative

MethodPercentage contribution
Coursework 50%
Exam  (2 hours) 50%

#### Referral

MethodPercentage contribution
Coursework 50%
Exam 50%

#### Repeat Information

Repeat type: Internal & External

### 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

Recommended texts for this module may be available in limited supply in the University Library and students may wish to purchase reading texts as appropriate.

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.