Unit name | Linear and Generalised Linear Models |
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Unit code | MATH30013 |
Credit points | 20 |
Level of study | H/6 |
Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
Unit director | Dr. Cho |
Open unit status | Not open |
Pre-requisites |
MATH11005 Linear Algebra and Geometry and MATH20800 Statistics 2 |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Unit Aims
Unit Description
The Linear Model is the ubiquitous model in Statistics. It is used extensively in experiments to evaluate interventions (e.g. medicine and public health, toxicology assessment, agricultural field trials, experimental psychology), and also to analyse observational data and make predictions. First half of this unit covers the theory and the practice of Linear Modelling, including least squares-based estimation and computation, model building, diagnostics, and the hypothesis testing, and use of the statistical computing environment R (most notably the 'lm' function and its methods).
Linear Modelling has its limitations, notably for quantities which are discrete. In healthcare, for example, we would like to model the response of a patient to a new treatment; typically this response is binary (yes/no, presence/absence). Or else, we would like to analyse count data, such as the number of occurrences of an event in a population, or for a person over a time interval. The second half of this unit provides an introduction to Generalised Linear Models explaining how it extends the normal distribution implicitly assumed in Linear Models to the much larger Exponential Family of distributions, which includes the Binomial and the Poisson distributions, among many others. The theory and the practice of Generalised Linear Model is covered, including the maximum likelihood-based estimation and computation, diagnostics and the hypothesis testing. The unit also covers practical aspects of fitting Generalised Linear Models in R (using the 'glm' function in R), including model choice, diagnostic checking, and prediction. Several important applications are considered in detail: binary responses, categorical responses (i.e., more than two levels) and count data.
Relation to Other Units
This unit builds on the basic ideas of linear models introduced in Statistics 1 and Statistics 2, and extends them to deal with more general specifications. Other related units are Bayesian Modelling and Theory of Inference.
Familiarity with the nature and common syntax of the Linear and Generalised Linear Models, and with their use in a variety of applications.
Experience of fitting and analysing the regression models in R.
The unit will be taught through a combination of
90% Timed, open-book examination 10% Coursework
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.
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