Next: MC380 Ordinary Differential Equations
Up: Year 3
Previous: MC347 Coding Theory
MC361 Generalized Linear Models
| Credits: 20 |
Convenor: Dr. M.J. Phillips |
Semester: 2 |
| Prerequisites: |
essential: MC160, MC260, MC264, MC265 |
|
| Assessment: |
Coursework: 20% |
Three-hour examination: 80% |
| Lectures: |
36 |
Classes: |
10 |
| Tutorials: |
none |
Private Study: |
104 |
| Labs: |
none |
Seminars: |
none |
| Project: |
none |
Other: |
none |
| Total: |
150 |
|
|
Explanation of Pre-requisites
The module MC160 provides the basic ideas of probability
which are required to understand statistical methods.
The module MC265 presents the basic concept of a statistic
and its use in estimation and hypothesis testing.
The module MC260 provides the techniques for study of the
joint distributions of random variables which enable the
classical normal theory results of mathematical statistics to be derived.
Then there is a brief introduction to
the basic methods of data analysis
based on the
classical normal theory results of mathematical statistics.
The module MC264 presents the basic methods of data analysis
based on the general linear model and the
theoretical results of this model.
Course Description
This module extends the ideas used in Linear Modelling
to a more general framework, which allows the possibility
of including a number of analyses in one general approach.
This occurs in the case when the response variable is dependent
through some link function on a predictor
of an unknown linear combination of the explanatory
variables as well as an error random variable.
With a suitable choice of link function and error structure
it is possible to cover,
within a general framework, a number of techniques for analysing
data:
linear modelling of continuous variables,
log-linear modelling
for the analysis of counts and proportions and
linear logistic regression modelling
for binary data.
Two prime objectives of an analysis using these models include
a determination of which explanatory variables are important,
and exactly how these variables are related to the response
variable. It is possible to associate confidence intervals to
estimates or predictions obtained from the model and
assign p-values to hypotheses to be tested.
The analysis of the model is based on the deviance which
offers a method for assessing the acceptability
of any proposed model.
Aims
This module aims to introduce the generalized linear model.
It presents the methods of
estimation of the linear model parameters and the methods of
making inferences about these parameters through the calculation of
confidence intervals and the use of hypothesis tests.
In particular it is an aim of this course to impart understanding
of how statistical models explain variation.
The aim of covering the
theory for the generalized linear model is to
understand the extension of the theory
to cover
log-linear models
for the analysis of counts and proportions and
linear logistic regression models for binary data.
Illustrations of how to use statistical software package GLIM
to analyse data using the generalized linear model are given.
Objectives
To present the assumptions made in using the
generalized linear regression model.
To enable the calculation of confidence intervals and
the use of hypothesis tests for model parameters.
To assess the fit of a log-linear model
using a nested hierarchy of log-linear models.
To understand the theory of the generalized linear model.
To understand how to use GLIM to analyse data with the
generalized linear model.
Transferable Skills
The ability to calculate estimates and make
inferences about the parameters of the
generalized linear regression model.
The ability to construct confidence intervals
and
to perform hypothesis tests for model parameters.
The ability to assess the
fit of a log-linear model using change in deviance.
Knowledge of the theory of the general linear model.
The ability to use GLIM to analyse data with the
generalized linear model.
Syllabus
Examples of two dimensional contingency tables.
Pearson goodness-of-fit test for 2 by 2 table.
Three sampling models. Maximum likelihood estimates (MLEs)
for the expected cell frequencies for
two dimensional contingency tables.
Properties of the odds ratio.
Likelihood ratio goodness-of-fit test statistic.
Partitioning two dimensional tables.
Three dimensional tables.
Hierarchical log-linear models for count data.
Maximum likelihood estimates (MLEs)
for the expected cell frequencies for
two dimensional contingency tables.
Bartlett's test.
Conditional likelihood ratio goodness-of-fit test statistic.
Theorem for collapsing tables. Birch's results.
A nested hierarchy of log-linear models.
Model choice.
Higher dimensional tables.
Stepwise selection procedures.
The theory of the generalized linear model.
Deviance. Residuals.
Models for binary data - linear logistic regression models.
Incomplete two dimensional contingency tables.
Fitting models in GLIM.
Reading list
Essential:
P. McCullagh and J. A. Nelder,
Generalized Linear Models,
2nd edition,
Chapman and Hall.
Details of Assessment
The final assessment of this module will consist of 20% coursework
and 80% from a three hour examination, which is OPEN BOOK, during the
Summer exam period. The 20% coursework contribution will be determined by
students' solutions to coursework problems. The examination paper will contain
6 questions with full marks on the paper obtainable from 4 complete answers.
Next: MC380 Ordinary Differential Equations
Up: Year 3
Previous: MC347 Coding Theory
S. J. Ambler
11/20/1999