MA208-5-SP: LINEAR MODELS
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to Study Abroad / Exchange Students: Yes Pre-requisites: EC252 OR MA108
|Module is taught during the following terms
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
- 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. Imputation of missing values.
- 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 & 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 groups.
30 per cent Coursework Mark, 70 per cent Exam Mark
Course work assessment: best 2 (each 2.5%) out of 4 problem sets; group project (written report and oral presentation) count for 25%.
Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework Information
Exam Duration and Period
2:00 hour exam during Summer Examination period.
Available to Socrates/IP students spending all relevant terms at Essex.
- Main texts:
Dobson, A. J., Barnett, A.G. (2008), An Introduction to Generalized Linear Models, 3rd edition, Chapman & Hall.
Andersen, E.B. (1998), Introduction to the Statistical Analysis of Categorical Data, Springer-Verlag.
Draper, N. R. and Smith, H. (1998), Applied Regression Analysis, 3rd edition, Wiley.
Fox, J. (1997), "Applied Regression Analysis, Linear Models, and Related
Robert I. Kabacoff (2011), R in Action - Data Analysis and Graphics with R, Manning Publications.
Krzanowski, K. (1998), An Introduction to Statistical Modelling, Arnold.
Sawitzki, G. (2009), Computational Statistics - An Introduction to R, Chapman & Hall.