Module Details

MA308-7-SP-CO: Linear Models

Year: 2016/17
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to Study Abroad / Exchange Students: No
Full Year Module Available to Study Abroad / Exchange Students for a Single Term: No
Outside Option: No

Staff
Supervisor:
Teaching Staff: Dr Hongsheng Dai, email hdaia@essex.ac.uk
Contact details: Miss Shauna McNally - Graduate Administrator. email: smcnally (Non essex users should add @essex.ac.uk to create the full email address), Tel 01206 872704

Module is taught during the following terms
Autumn Spring Summer

Module Description


Aims

To bring together and develop the ideas concerning regression, the analysis of variance, the analysis of contingency tables, under the common umbrella of the general linear model.

On completion of the course students should be able to:

- represent a model in matrix form
- write down and manipulate matrix expressions for least squares estimates and their properties
- appreciate the problems of model selection and know standard methods such as backward elimination
- be able to formulate a test procedure for handling a discrete random variable
- understand what is meant by log-linear model and how it applies to multidimensional contingency tables
- use R for data analysis


Syllabus:

- General linear model: least Squares, properties of estimators, Gauss-Markov theorem, ANOVA, interval estimates of parameters, WLS, linearising.
- Multiple regression: regression diagnostics, residuals, leverage and influence, AIC, Mallows' Cp.
- Logits and logistic regression: Newton-Raphson method, fit of the model, hypothesis testing, diagnostics and polytomous response variables.
- Log-linear models: two-, three- and multi-way contingency tables, Deming-Stephan algorithm, hypothesis testing, choice of model, diagnostics and model search.

Learning and Teaching Methods

The module runs at 3 hours (2 lectures, 1 class or lab) per week in the spring term. In the summer term 3 revision lectures are given. A project is undertaken in small groups. Coursework consists of problem sheets, mini tests, a project report and presentation.



Assessment

30 per cent Coursework Mark, 70 per cent Exam Mark

Coursework

30 percent coursework mark consisting of best 2 (each 2.5%) out 4 problem sets; a group project (written report and oral presentation) counting for 25%.

Other details

Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework and Test Information

Exam Duration and Period

2:00 during Summer Examination period.

Bibliography

  • Recommended reading:
  • Dobson, A. J., Barnett, A.G. (2008), An Introduction to Generalized Linear Models, 3rd edition, Chapman & Hall.
  • Faraway, J.J. (2004), Linear Models with R, Chapman & Hall. UK.
  • Supplementary texts:
  • Andersen, E.B. (1998), Introduction to the Statistical Analysis of Categorical Data, Springer-Verlag.
  • Armitage, P., Berry, G., Matthews, J.N.S., Statistical methods in medical research, (4th edition), Wiley, Chichester, UK, 2001.
  • Draper, N. R. and Smith, H. (1998), Applied Regression Analysis, 3rd edition, Wiley.
  • Kabacoff, R.I., R in Action - Data Analysis and Graphics with R, Manning Publications Co, 2011.
  • Krzanowski, K. (1998), An Introduction to Statistical Modelling, Arnold.

Further information