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 |
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:
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).
By the end of the unit, the student should have a good understanding of
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.
Lectures, examples and homework problems.
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.
The range of topics covered in the unit is rather broad. Students might find the following textbooks useful:
Other useful references include: