The University of Southampton
Courses

# STAT6083 Generalised Linear Models

## Module Overview

This module aims to introduce students to a wide range of statistical models grouped by the unifying theory of Generalized Linear Models: Linear, Logistic, Multinomial, Cumulative Ordinal and Poisson regression, as well as Log-linear models are presented, with emphasis on the underpinning theory and practical examples. Students are also exposed to the basic foundations of estimation for GLMs.

### 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

The module is divided in 4 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. Depending on time, more advance regression topics, such as Robust regression, data driven transformations, Non-parametric regression, kernel, and spline models may be briefly introduced.

### 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
Independent Study160
Teaching40
Total study time200

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

Faraway, J. J. (2016). Extending the linear model with R: generalized linear, mixed effects and nonparametric regression models.

Fox, J., Sanford, W. (2019). An R Companion to Applied Regression.

Agresti, A. (2013). Categorical Data Analysis.

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

Faraway, J. J., (2015). Linear Models with R.

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

### 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.