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Unit information: Linear and Generalised Linear Models in 2018/19

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Unit name Linear and Generalised Linear Models
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

Linear Algebra and Geometry (MATH11005), Probability 1 (MATH11300), Statistics 1 (MATH11400) and Statistics 2 (MATH20800)

Co-requisites

None

School/department School of Mathematics
Faculty Faculty of Science

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.

Unit aims:

1. To provide students with the definition of linear models and theoretical treatment of the least squares estimation using QR decomposition for statistical inference.
2. To provide students with the definition of generalised linear models and theoretical treatment of the maximum likelihood estimation.
3. To demonstrate the procedure of model fitting including model diagnosis, stepwise model building and interpretation of the results.
4. To enable students to use 'lm', 'glm' and related functions in R to handle the computational aspects of model fitting.
5. To provide students with a brief introduction to penalised least squares methods for handling 'big data'.

Intended learning outcomes

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.

Teaching details

Lectures supported by regular formative problem and solution sheets + 2 computer labs. Plus office drop in sessions.

Assessment Details

100% examination (2.5 hours)

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.

Reading and References

Recommended:

N.R. Draper and H. Smith, Applied Regression Analysis, 3rd ed., John Wiley & Sons Inc, 1998.

S. Wood, Core Statistics, Cambridge University Press, 2015.

P. McCullagh, J. A. Neider, Generalized Linear Models, Chapman and Hall, 1983.

A. C. Dobson, Introduction to statistical modelling, Chapman and Hall, 1983.

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