MA37510 - LINEAR MODELLING TECHNIQUES

Module Identifier	MA37510
Module Title	LINEAR MODELLING TECHNIQUES
Academic Year	2002/2003
Co-ordinator	Mr Alan Jones
Semester	Semester 2
Pre-Requisite	MA36510
Course delivery	Lecture	19 x 1 hour lectures
	Seminars / Tutorials	3 x 1 hour example classes
Assessment	Semester Exam	2 Hours (written examination)	100%
	Supplementary Assessment	2 Hours (written examination)	100%

Learning outcomes

On completion of this module, a student should be able to:

explain and use the reduction in sum of squares principle;
formulate and carry out a test of a linear hypothesis;
explain the importance of good design matrix structures;
compare different models suggested for the same data sets;
construct and fit models involving coincident or parallel straight lines as arise in biological and pharmaceutical assays;
analyse a design matrix with respect to leverage;
fit models of less than full rank;
explain the idea of estimability;
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 models. 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.

Reading Lists

Books
** Recommended Text
R H Myers and J S Milton. (1991) A first course in the theory of linear statistical models. PWS-Kent 0534916457
** Supplementary Text
F A Graybill. (1976) Theory and application of the linear models. Duxbury 0878721088