Module Identifier MA37510
Module Title LINEAR MODELLING TECHNIQUES
Co-ordinator Mr Alan Jones
Semester Semester 2
Other staff Mr Alan Jones
Pre-Requisite MA36510
Course delivery Lecture   19 Hours. (19 x 1 hour lectures)
Seminars / Tutorials   3 Hours. (3 x 1 hour example classes)
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours (written examination)  100%
Supplementary Assessment2 Hours (written examination)  100%

Learning outcomes

On completion of this module, a student should be able to:
1. explain and use the reduction in sum of squares principle;
2. formulate and carry out a test of a linear hypothesis;
3. explain the importance of good design matrix structures;
4. compare different models suggested for the same data sets;
5. construct and fit models involving coincident or parallel straight lines as arise in biological and pharmaceutical assays;
6. fit models of less than full rank;
7. explain the idea of estimability;
8. describe the concept of a generalized linear model and, in some appropriate situations, construct and fit suitable models.

Brief description

This module builds on the work in MA36510 by focusing on some of the many and varied applications of the Linear Model and considers techniques and modifications that have been motivated by them. Modern developments in the area are also considered.

Aims

To make the student aware of some of the applications of Linear Models and to consider new developments.

Content

1.FURTHER CONSIDERATION OF THE LINEAR MODEL: The general linear hypothesis; reduction in sum of squares principle. Correlated and/or heteroscedastic observations. The Generalized Gauss Markov Theorem. Non-invertible designs. One and two-way layouts. Examples.
2. COMPARISON OF MODELS: Orthogonality. Orthogonal polynomials. Weighing designs. Brief treatment of design optimality.
3. GENERALIZED LINEAR MODELS: Basic ideas. The exponential family. Link functions and canonical links. Deviance and deviance residuals. Examples including models for exponential, binomial and Poisson data.