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Generalised Linear Models 34 (MATH M5200)

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Administrative Information

  1. Unit number and title: MATH M5200 Generalised Linear Models 34
  2. Level: M/7
  3. Credit point value: 10 credit points
  4. Year: 12/13
  5. First Given in this form: 2008-2009
  6. Unit Organiser: Heather Battey
  7. Lecturer: Dr Heather Battey
  8. Teaching block: 2
  9. Prerequisites: MATH 20800 Statistics 2, MATH 35110 Linear Models

Unit aims

To study both theoretical and practical aspects of statistical modeling, to develop the expertise in selecting and evaluating the model and interpreting the results.

General Description of the Unit

The course is focused on multivariate regression methods with univariate independent outcomes that can take on continuous or categorical values.The topics discussed include:

  • Model selection, parameter estimation, diagnostics, results interpretation.
  • Methods for estimating the standard error. 
  • Regression models for lifetime data.

Relation to Other Units

This unit builds on the basic ideas of linear models introduced in Statistics 1 (MATH 11400) and Linear Models (MATH 35110), and extends them to deal with more general specifications.

Teaching Methods

Lectures, examples and homework problems.

Learning Objectives

By the end of the unit, the student should have a good understanding of

  • principles of statistical modelling: response and explanatory variables, systematic and random variation, independence and conditional independence;
  • methods of inference: maximum likelihood;
  • methodology of generalized linear models and survival analysis;
  • advance use of the statistical software system (R).

Assessment Methods

The final assessment mark for Generalized Linear Models level M is 80% from a 1 ½-hour written examination in May/June and 20% from the designated coursework assignments.

The three coursework assignments will contain both theoretical and practical questions. No group work for the coursework assignments is permitted.  

The final examination consists of THREE questions. A candidate's best TWO answers will be used for assessment. Calculators of an approved type (non-programmable, no text facility) are allowed. From 2012-13 ONLY calculators carrying a 'Faculty of Science approved' sticker will be allowed in the examination room. Statistical tables will be provided.

Award of Credit Points

Credit points are gained by:

  • either passing the unit,
  • or getting a final assessment mark of 30 or over and getting 30 or over on the coursework assignments. 

Transferable Skills

The ability to analyze relatively complex data sets that includes exploratory data analysis, model formulation, statistical computing, model evaluation, diagnostics and the ability to interpret the results for the general audience. 

Texts

The range of topics covered in the unit is rather broad. Students might find the following textbooks useful

  • W J Krzanowski, An Introduction to Statistical Modelling, Arnold, 1998.

  • P McCullagh, J A Nelder, Generalized Linear Models, Chapman and Hall, 1983.

  • A C Dobson, Introduction to statistical modelling, Chapman and Hall, 1983.

  • D R Cox and D Oakes, Analysis of survival data, Chapman and Hall, 1984.

Other useful references include  

  • W N Venables and B D Ripley, Modern applied statistics with S-Plus, Springer, 1994.

  • J Fox. An R and S-Plus Companion to Applied Regression, Sage Publications, 2002.

  • B A Everitt, T Hothorn, A Handbook of Statistical Analysis Using R, Chapman&Hall, 2006.

 

Syllabus

Overview of data analysis, motivating examples. Review of linear models. (1 lecture)

Generalized linear models (GLMs). Exponential family model, sufficiency issues. Link function, canonical link. (5 lectures)

Inference for generalized linear models, based on asymptotic theory: confidence intervals, hypothesis testing, goodness of fit. Results interpretation. Diagnostics. (4 lectures)

Binary responses, logistic regression, residuals and diagnostics. (2 lectures)

Introduction to survival analysis. Distribution theory: standard parametric models. Proportional odds model and connection to binomial GLM's. Inference assuming a parametric form for the baseline hazard. (4 lectures)

Note: the number of lectures for each topic is approximate.