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MA3201 Generalized Linear Models

MA3201 Generalized Linear Models

Credits: 20 Convenor: Dr. M.J. Phillips Semester: 2 (weeks 1 to 12)
Prerequisites: essential: MA1061, MA2201, MA2261
Assessment: Examination and coursework: 80:20% Examination: 0%
Lectures: 36 Problem Classes: 10
Tutorials: none Private Study: 104
Labs: none Seminars: none
Project: none Other: none
Surgeries: none Total: 150

Subject Knowledge

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.

Learning Outcomes

Students should know the assumptions made in using the generalized linear regression model and be able to calculate confidence intervals and use hypothesis tests for model parameters. Also be able to assess the fit of a log-linear model using a nested hierarchy of log-linear models. Students should be able to understand the theory of the generalized linear model and be able to understand how to use GLIM to analyse data with the generalized linear model.

Methods

Class sessions with some handouts.

Assessment

Marked problem sheets and examination.

Subject Skills

Aims

To provide students with the ability to calculate estimates and make inferences about the parameters of the genralized linear model, and assess the fit of these models, as well as the knowledge of the theory of the generalized linear model.

Learning Outcomes

Students will have the ability to calculate estimates and make inferences about the parameters of the generalized linear regression model as well as the ability to construct confidence intervals and to perform hypothesis tests for model parameters. Students will be able to assess the fit of a log-linear model using change in deviance, knowledge of the theory of the general linear model, and the ability to use GLIM to analyse data with the generalized linear model.

Methods

Class sessions.

Assessment

Marked problem sheets and examination.

Explanation of Pre-requisites

The module MA1061 provides the basic ideas of probability which are required to understand statistical methods. The module MA2201 presents the basic concept of a statistic and its use in estimation and hypothesis testing. 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 MA2261 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.

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

Recommended:

P. McCullagh and J. A. Nelder, Generalized Linear Models, 2nd edition, Chapman and Hall, 1989.


Resources

Problem sheets, computer laboratory, lecture rooms.

Module Evaluation

Module questionnaires, module review, year review.

Next: MA3501 History of Mathematics Up: ModuleGuide03-04 Previous: MA3151 Topology

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Last updated: 2004-02-21
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