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    • MTH6134 First quiz
    • MTH6134 Second quiz
    • Main exam 2023-2024 Quiz

      This assessment is intended to be completed within 3 hours. Although you are expected to finish the assessment within this time frame, you will be given an additional 30 minutes for scanning and submitting your handwritten solution in case you have not already done so.

      IMPORTANT – If you run out of time during this assessment, we will not accept IT issues as an extenuating circumstance. This is because we have given you ample time to complete and submit your work. If your attempt is still in progress at the end of the set time slot, any file you have uploaded will be automatically submitted.

  • Week 1 :

    Overview: This week is the initial set up of the course. We do a gentle introduction to the Module, including looking at the SEATTLE Heart Failure Model and the MAGGIC model as motivating examples. We then looked at specific distributions and link functions.

    Lectures

    Pages 1-2 of the typed notes.

    Tutorial

    No tutorial.

    Exercises

    No exercises.

    Extras


  • Week 2 :

    Overview: This weeks material concludes the overview of distributions and link functions to then start with the topic of likelihood. We study likelihood using the material of multivariate linear regression as guiding theme.

    Lectures

    Pages 2-5.

    Tutorial

    This tutorial (R lab) is a refresher on linear regression.

    Exercises

    Try Exercises 1,2, 8 (parts 1-3) and 4,5.

    Extras


  • Week 3:

    Overview: The study of linear regression continues. We look at it from the point of view of likelihood.

    Lectures

    Pages 6-9.

    Tutorial

    This (R) lab is an exercise on multiple regression.

    Exercises

    Try exercises 13 (regression through the origin), 18 (binomial) and 19 (Poisson).

    Extras



  • Week 4:

    Overview: Having completed our review of regression via likelihood, we look at tests based upon likelihood ratios. Time permitting, we will start looking at the family of exponential distributions.

    Lectures

    We look at likelihood ratio tests and at Wilk's theorem. Students are recommended to look in detail at Example 2.8.

    Tutorial

    The lab has a first look at regression of binomial data, exploring different link functions.

    Exercises

    We will look at Exercises 21, 23 and 25.

    Extras


  • Week 5:

    Overview: This week we concentrate on the core topic of the Module as well as distributions of the exponential family.

    Lectures

    We start the core topic of the Module which are Generalized Linear Models (GLMs).

    Exercises

    We have a first look at exponential distributions, doing exercise 28 and 29 for binomial and negative binomial distributions.

    Extras


  • Week 6:

    Overview: This week we continue our study of GLMs, with view on estimation.

    Lectures

    The material continues with Pages 13-15.

    Tutorial

    The tutorial has a look at empirical link-transformation of the response as a vehicle for checking the fit of model to data.

    Exercises

    The emphasis is in computation of Fisher information matrix, exercises 31 and 34.

    Extras

  • Week 7: (midterm week)

    This week we have no lectures and the midterm test on Thursday 091123 between 1000-1100. You can read the information that has been posted in the announcements section, reachable from this link https://test.qmplus.qmul.ac.uk/mod/forum/discuss.php?d=500762

    • Some questions, put as test File

      Here is a sample 'quiz', based upon some exercises. Read the following very carefully:
      We have practiced this material for quite some weeks now. If you have not put an equivalent time doing the usual Module activities (attending lectures, doing the exercises and the tutorial/labs), then you have quite a bit of ground to catch up before you are in a suitable condition for a decent result in the midterm. None of the course material is hard, but you need to be familiar with it.
      The 'mock exam' has (for now) no solutions, which I'll put tomorrow.

      104.4 KB
    • ... and the solutions File

      are here. Of course, the true proof of knowing whether you know the topic is that you mark your own attempt.

      133.1 KB

  • Week 8:

    Overview: This week we complete the development of the topic of GLM with a second take on estimation and residuals.

    Lectures

    Pages 14-18 of notes.

    Tutorial

    The lab is concentrated on a Poisson regression for the cloth data set.

    Exercises

    We look at the GLM against maximal models, this is exercise 38.

    Extras


  • Week 9:

    Overview: With a change of timetable to Wednesday, this week we continue our examination of binary response data.

    Lectures

    We look at pages 19-22.

    Tutorial

    We will analyze the data in file rat.csv.

    Exercises

    We look at residuals in exercise 39 and modelling in exercises 40 and 43.

    Extras


  • Week 10:

    Overview: This week we conclude GLMs for binary data and start covering count data regression.

    Lectures

    We are covering pages 21-23 of the lecture notes.

    Tutorial

    The tutorial of this week involved a Poisson model with two means, which was contrasted (compared) with the Poisson model with a single mean, that is, the null model.

    Exercises

    Exercise #43 is concerned with Poisson regression and a two factor model.

    Extras

    As an extra for exercise #43, what if you analize considering (incorrectly) numerical values for the two factors of interest?

  • Week 11:

    Overview:  This week we continue the topic of contingency tables. Time permitting, we will look at exponential regression.

    Lectures

    We look at pages 24-27 of the notes.

    Tutorial

    The tutorial continues with analysis of contingency tables in R.

    Extras


  • Module description

    The module builds on theory already taught in Statistical Modelling I and develops the general theory of linear models. You will be able to fully undertand the concept of the generalised linear models, which can be used in problems where a normal distribution is not appropriate, such as when working with binary or count data. In the lab sessions, you will be able to learn how to apply these modelling techniques in real-world problems by programming in R. 

  • Syllabus

    • 1 Introduction
      2 Normal linear model (regression)
      3 Generalized linear models (GLMs)
      4 Binary data (logistic regression)
      5 Count data (Poisson regression)
      6 Survival data (exponential regression)

  • Module aims and learning outcomes

    At the end of this module, students should be able to:

    • Derive the likelihood, the likelihood equations and the Fisher information matrix, for a given regression model.
    • Carry out likelihood ratio tests.
    • Identify probability distributions belonging to an exponential family and adapt a description as a generalised linear model.
    • Describe numerical procedures for estimation in generalised linear models.
    • Explain the important theorems in probability theory utilised in test procedures in generalised linear models.
    • Analyse data sets following binomial or Poisson distributions.
    • Estimate parameters and test hypotheses in generalised linear models by means of R.

  • Assessment

    This Module is to be evaluated with two in term tests (weeks 7 and 12), each test worth 10% of the Module total. There will be a final exam (in January) which will count for 80% of the Module mark.

  • Module handbook

    This is the basic Module material, introducing to Generalized Linear  Models (GLMs). There may be some (minor) amendments to the typed notes during the term.

  • Some extras

  • General course materials

    We provide a pdf document with exercises for the Module for you to practice and discuss in lectures. This file may be amended during the term so always look at the qmplus version. 

    We'll also provide here some selected solutions to exercises and labs. Note that a) you are still required to work on exercises before looking at the contents of this file, b) some solutions are still left for you as exercises and importantly c) the files is to be updated as weeks go along, so always come back here for a fresh copy. The file will be your only source of exercises and solutions, look no further!

    We also store here the R lab (tutorial) material used every week.

  • Exam papers

    In this space there will be some exam samples. Be aware that any past exam material made available implies *no* promise nor indication that future exam material will be identical.

    Note that MTH6134 exams in repositories with date prior to 2019 (inclusive of that year) were for a different syllabus. (If you look at the material of those exams closely, all are gaussian glms with categorical variables ... but in any case the material is relatively specialized to that model and therefore, not relevant to the glm syllabus).

  • Week 12:

    Overview: This week we conclude the Module looking at Survival data

    Lectures

    The lectures will cover part 6 of the notes.

    Tutorial

    The tutorial looked at leukaemia data with exponential regression.

    Exercises

    We looked at constrained estimation, concluding the material on contingency tables.

    Extras


  • Early feedback questionnaire

  • Assessment information

    • Assessment Pattern -  The assessment pattern of this module consists of  two courseworks (online in term tests) worth 10% each, a final exam worth 80%.

      Format and dates for the in-term assessments - The online in term tests will be in weeks 7 and 12. The main exam, also online will be in the January examination period.

      Format of final assessment - Your final examination will be online.  It will be 3 hours in duration with SpLD accommodations handled separately. 

      link to past papers - past paper exam repository

      Description of Feedback - 

    • Past papers Database

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