Unit information: Generalised Linear Models 34 in 2013/14

Unit name	Generalised Linear Models 34
Unit code	MATHM5200
Credit points	10
Level of study	M/7
Teaching block(s)	Teaching Block 2C (weeks 13 - 18)
Unit director	Dr. Liverani
Open unit status	Not open
Pre-requisites	None
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

We study methods for the analysis of data in which one variable, the response, is influenced systematically by one or more explanatory variables, which could be qualitative or quantitative in nature, in addition to the presence of random variation. In contrast to traditional methods involving linear models and normal variation, here we depart from linearity and normality. Instead of relying on least squares we employ the principle of maximum likelihood, but also investigate alternatives based on the idea of sparsity.

The topics discussed will be:

• Generalized linear models: extensions of the ideas of linear modelling to deal with situations where the response variable takes integer or categorical values. These methods are particularly important in biomedical applications. We also look into model validation and develop robust strategies to detect departures from the model like outliers.

• Survival analysis: an introduction to regression models for lifetime data, used in clinical trials and industrial testing.

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.

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.

Relation to Other Units

This unit builds on the basic ideas introduced in Probability and Statistics 1 (MATH 11340), and Linear Models (MATH 35110).

Intended Learning Outcomes

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).

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.

Teaching Information

Lectures, examples and homework problems.

Assessment Information

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. Statistical tables will be provided.

Reading and References

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.