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The University of Southampton

MATH6169 Flexible Regression

Module Overview

This module will introduce and develop flexible statistical modelling methods that allow for general and complex forms of data to be modelled, extending ideas already encountered in earlier modules on linear and/or generalised linear modelling. The two main foci of the syllabus will be methods for modelling grouped data using random effects, and non-parametric “smoothing” methods for modelling data with complex functional form.

Aims and Objectives

Module Aims

The aims of the module are: to study general-purpose methods for modelling complex data structures and apply them in practice using statistical software.

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

  • Understand and apply basic criteria that define successful statistical modelling.
  • Understand the concept of random effects, and their role in modelling common forms of grouped data.
  • Apply common nonparametric modelling methods to data with both single and multiple predictor variables.
  • Understand the theoretical underpinnings of the discussed modelling methods, and their implementation in appropriate statistical software.


- Fundamentals of random effect modelling and population versus subject-specific models. - Linear mixed models for continuous data, generalised least squares and restricted maximum likelihood. - Generalised linear mixed models for discrete data, likelihood estimation and numerical methods. - Common univariate smoothing methods including kernel smoothing and smoothing splines. - Generalised additive models. - Cross-validation and bias-variance trade-off for selecting smoothing parameters.

Learning and Teaching

Teaching and learning methods

36 Lectures and/or problem classes.

Independent Study114
Total study time150

Resources & Reading list

Faraway, J. J. (2016). Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models.. 

Wood, S. N. (2017). Generalized Additive Models: An Introduction with R. 

Demindenko, E. (2013). Mixed Models: Theory and Applications with R. Wiley.. 


Assessment Strategy

The assessment for the repeat candidates will be based completely on the final examination.


MethodPercentage contribution
Coursework 50%
Exam 50%


MethodPercentage contribution
Exam 100%

Repeat Information

Repeat type: Internal & External

Linked modules

pre-requisite: (MATH2010 and MATH3091) or STAT6083


Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at

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