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.
- Understand the foundation theory of Generalised Linear Models.
- Interpret the results of the modelling.
- Use a range of popular statistical models for continuous and categorical data.
- Use the statistical software package R to fit statistical models.
- Summarise data with an appropriate statistical model.
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.
|Total study time||200|
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
Agresti, A. (2007). An Introduction to Categorical Data Analysis. Wiley.
Faraway, J. J., (2015). Linear Models with R. CRC Press.
Fox, J., Sanford, W. (2019). An R Companion to Applied Regression. Sage Publications.
Faraway, J. J. (2016). Extending the linear model with R: generalized linear, mixed effects and nonparametric regression models. CRC Press.
Agresti, A. (2013). Categorical Data Analysis. Wiley.
Fox, J. (1997). Applied Regression Analysis, Linear Models, and Related Methods. Sage Publications.
Dobson, A. J. (2008). An Introduction to Generalized Linear Models. Chapman & Hall.
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