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
Having successfully completed this module you will be able to:
- 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.
- Summarise data with an appropriate statistical model.
- Interpret the results of the modelling.
- Use the statistical software package R to fit statistical models.
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.
Learning and Teaching
Teaching and learning methods
Teaching will be delivered by a mixture of synchronous and asynchronous online methods, which may include lectures, quizzes, discussion boards, workshop activities, exercises, and videos. A range of resources will also be provided for further self-directed study. Face-to-face teaching opportunities will be explored depending on circumstances and feasbility.
|Total study time||150|
Resources & Reading list
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.
Dobson. A.J (2008). An Introduction to Generalized Linear Modules. Chapman and Hall.
Fox, J (1997). Applied Regression Analysis, Linear Models, and Related Methods. Sage Publications.
Agresti, A (2013). Categorical Data Analysis. Wiley.
Faraway, J,J (2015). Linear Models with R. CRC Press.
Faraway, J,J (2016). Extending the linear model with R: generalized linear, mixed effects and nonparametric regression models. CRC Press.
Agresti. A (2007). An Introduction to Categorical Data Analysis. Wiley.
Fox, J Sandford, W (2019). An R Companion to Applied Regression. Sage Publications.
There will be opportunities to evaluate your progress through formative assessment, with summative assessment based on two online assignments.
This is how we’ll formally assess what you have learned in this module.
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Repeat type: Internal & External