Generalised Linear Models

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

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

The module is divided in five parts 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 and Ordinal Responses and Logistic Regression:

One-way contingency tables, two-way contingency tables, measures of association, odds ratios and properties of odds ratios, binary logistic regression, multinomial logistic regression, ordinal logistic regression, maximum likelihood estimation, 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, log-linear models for multi-way contingency tables, Simpson’s paradox, residual analysis, model selection, deviance and likelihood ratio tests.

Part 5. Overdispersion in GLMs:

Detecting overdispersion, handling overdispersion, quasi-likelihood approach, two-stage generation process, testing for overdispersion.

Teaching and learning methods

Teaching will be through a combination of lectures, computer workshops and tutorials. 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.

Exercises on the theory will be discussed in the tutorials.

Resources & Reading list

General Resources

Software requirements. You will require access to R, which is available on the University’s workstations and can be downloaded to your own computer for use with your studies.

Textbooks

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

Agresti, A. (2015). Foundations of Linear and Generalized Linear Models. Wiley.

Dobson, A.J. and Barnett, A.G. (2008). An Introduction to Generalized Linear Modules. CRC Press.

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

Faraway, J.J. (2016). Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models. CRC Press.

Fox, J. and Sandford, W. (2019). An R Companion to Applied Regression. Sage Publications.

James, G., Witten, D., Hastie, H. and Tibshirani, R. (2021). An Introduction to Statistical Learning with Applications in R. New York: Springer.

Agresti, A. (2019). An Introduction to Categorical Data Analysis. Wiley.

Fox, J. (2016). Applied Regression Analysis, Linear Models and Generalized Linear Methods. Sage Publications.

Assessment strategy

There will be opportunities to evaluate your progress through formative assessment. The summative module assessment will consist of a piece of individual coursework and a two-hour exam. Each of these will be worth 50% of the overall mark.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat Information

Repeat type: Internal & External