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Generalised Linear Models (MATH 35200)

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Administrative Information

  1. Unit number and title: MATH 35200 Generalised Linear Models
  2. Level: H/6
  3. Credit point value: 10 credit points
  4. Year: 12/13
  5. First Given in this form: 1999-2000
  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.
  • An introduction to 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 (including both theory and examples) and practice problems.

Learning Objectives

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

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

Assessment Methods

The assessment mark for Generalized Linear Models is calculated from a 1 ½-hour written examination in May/June consisting 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 mark of 30 or over, and also handing in satisfactory attempts at three designated homework questions.

Transferable Skills


Model selection and data analysis. Statistical computing skills. Results interpretation. 

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.