Overview

Preface

These lecture notes are produced for the University of Leeds module “MATH5824 - Generalised Linear and Additive Models” for the academic year 2023-24. They are based on the lecture notes used previously for this module and I am grateful to the previous module leader Robert Aykroyd for sharing his notes and the considerable effort he made in developing these. A PDF version will be made available on the University of Leeds Minerva system. This will be my first year teaching this module, so I encourage you to offer feedback that can be used to improve the content throughout the semester.

RP Mann, Leeds, January 6, 2025

Generative AI usage within this module

The assessments for this module fall in the red category for using Generative AI which means you must not use Generative AI tools. The purpose and format of the assessments makes it inappropriate or impractical for AI tools to be used.


Warning

Statistical ethics and sensitive data
Please note that from time to time we will be using data sets from situations which some might perceive as sensitive. All such data sets will, however, be derived from real-world studies which appear in textbooks or in scientific journals. The daily work of many statisticians involves applying their professional skills in a wide variety of situations and as such it is important to include a range of commonly encountered examples in this module. Whenever possible, sensitive topics will be signposted in advance. If you feel that any examples may be personally upsetting then, if possible, please contact the module lecturer in advance. If you are significantly effected by any of these situations, then you can seek support from the Student Counselling and Wellbeing service.


Official Module Description

Module summary

Linear regression is a tremendously useful statistical technique but is limited to normally distributed responses. Generalised linear models extend linear regression in many ways - allowing us to analyse more complex data sets. In this module we will see how to combine continuous and categorical predictors, analyse binomial response data and model count data.A further extension is the generalised additive model. Here, we no longer insist on the predictor variables affecting the response via a linear function of the predictors, but allow the response to depend on a more general smooth function of the predictor.

Objectives

On completion of this module, students should be able to:

  • carry out regression analysis with generalised linear models including the use of link functions, deviance and overdispersion;
  • fit and interpret the special cases of log linear models and logistic regression;
  • compare a number of methods for scatterpot smoothing suitable for use in a generalised additive model;
  • use a backfitting algorithm to estimate the parameters of a generalised additive model;
  • interpret a fitted generalised additive model;
  • use a statistical package with real data to fit these models to data and to write a report giving and interpreting the results.

Syllabus

Generalised linear model; probit model; logistic regression; log linear models; scatterplot smoothers; generalised additive model.

University Module Catalogue

For any further details, please see MATH5824 Module Catalogue page