Flexible Regression | MATH6169 | University of Southampton

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.

Linked modules

pre-requisite: (MATH2010 and MATH3091) or STAT6083

Aims and Objectives

Learning Outcomes

Having successfully completed this module you will be able to:

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

Syllabus

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.

Study time
Type	Hours
Independent Study	114
Teaching	36
Total study time	150

Resources & Reading list

Textbooks

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

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

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

Assessment

Assessment strategy

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

Formative

This is how we’ll give you feedback as you are learning. It is not a formal test or exam.

Examination Assignments and problem sheets

Summative

This is how we’ll formally assess what you have learned in this module.

Breakdown
Method	Percentage contribution
Coursework	50%
Examination	50%

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Breakdown
Method	Percentage contribution
Examination	100%

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.

Breakdown
Method	Percentage contribution
Examination	100%

Repeat Information

Repeat type: Internal & External