Module Catalogue 2026/27

Pre Requisite Comment

N/A

Co Requisite Comment

N/A

Aims

Aims
To achieve an understanding of linear models, and how regression, Analysis of Variance (ANOVA)
and Analysis of Covariance (ANCOVA) models arise as special cases. To understand the problem of
identifiability in ANOVA, and the role played by parameter constraints and dummy variables in
solving it. To achieve an understanding of Generalized Linear Models and achieve familiarity with
the most common families, understanding how logistic regression and log linear models arise as
special cases. To understand the Exponential family and demonstrate that certain distributions
belong to this.
Module summary
This module is concerned with building and applying statistical models for data. How does a mixture
of quantitative and qualitative variables affect the body mass index of an individual? Suppose we
find an association between age and body mass index, how can we study if this association varies
between men and women, or between those with different educational backgrounds? In this course
we consider the issues involved when we wish to construct realistic and useful statistical models for
problems which can arise in a range of fields: medicine, finance, social science, sport and
environmental issues being some of the main areas.
We revise multiple linear regression models and see how they are special cases of a general linear
model. We move on to consider Analysis of Variance (ANOVA) as another special case of a general
linear model – this is the problem of investigating contrasts between different levels of a factor in
affecting a response and then we generalize to the case of several factors. We consider Analysis of
Covariance (ANCOVA) which involves mixing linear regression and factor effects, and the idea of
interaction between explanatory variables in the way they affect a response.
We build on linear modelling by introducing a generalised framework of models which allow us to
move away from normally distributed errors to different kinds of random outcomes, building in an
appropriate transformation of the linear function of explanatory variables to match. This leads to the
topic of Generalized Linear Models, allowing us to study many different types of outcome measure
which could not have been handled using general linear models. We study the special cases
involved with Binomial outcomes, logistic regression, where we are interested in how explanatory
variables affect the success rate, and then log-linear models.
The module provides a comprehensive introduction to the issues involved in using statistics to model
real data, and to draw relevant conclusions. There is an emphasis on hands-on application of the
theory and methods throughout, with extensive use of R

Outline Of Syllabus

The general linear model: maximum likelihood in the multi-parameter case; estimation of parameters;
prediction; model adequacy; regression, ANOVA and ANCOVA as special cases. Model choice.
Analysis of designs with 1, 2 or 3 factors. Model identifiability, parameter constraints and dummy
variables. Use of transformations. Generalized linear models: overall construction as generalization of
linear models; binomial regression with various links; Poisson regression; log-linear models The
Exponential family of distributions. Various extended examples of statistical modelling using R.

Intended Knowledge Outcomes

Students will know the theory and techniques of modelling normal outcomes in terms of categorical
and continuous covariates using the general linear model. The students will extend their
knowledge of general linear models to encompass outcomes from several non-Normal Exponential
family distributions. They will understand the Exponential family of distributions.

Intended Skill Outcomes

The ability to determine the appropriate statistical model to use, to be able to use R to fit the model and to be able to interpret the fitted model. The ability to identify the kind of design and modelling approaches needed to address a wide variety of real-life statistical problems, and the ability to implement appropriate statistical modelling procedures using R.

Students will develop skills across the cognitive domain (Bloom's taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate and create.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one way for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem-solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; the summative assessment has a secondary formative purpose as well as its primary summative purpose.

General Notes

N/A