MAS6003 Linear Modelling

Note: This is an old module occurrence.

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 Both semesters, 2012/13 20 Credits Lecturer: Dr Kevin Walters uses MOLE Timetable Reading List Aims Outcomes Teaching Methods Assessment Full Syllabus

The unit develops students' understanding of the general theory of linear models for regression modelling and analysing experiments, and introduces extensions to these models. Many important applications are considered, including the modelling of binary and count data, and the analysis of contingency tables and structured data. Discussion in the unit covers regression model building and model checking, multiple regression and the analysis of complete factorial experiments. It then considers mixed effects models, which are useful when the data are structured, with different levels of variation. Finally, it discusses Generalized Linear Models, which are convenient to use in many non-standard applications.

There are no prerequisites for this module.
No other modules have this module as a prerequisite.

Outline syllabus

• Semester 1: Linear Models
• Simple Linear Regression
Brief introductory examples on regression and the analysis of variance.
• General Linear Model
The general linear model; reduced models; replicates and lack of fit; weighted and generalized least-squares.
• Diagnostics and Model Revision
Examination of residuals; types of residuals; influential observations; transformations.
• More Linear Models and Model Building
Use of the flexibility of the general linear model; strategy for model-building and variable selection.
• Validation of Regression Models
Validation techniques, data from planned experiments.
• Semester 2: Extended Linear Models
• Review of Linear Models
• Mixed Effects Models
Mixed Effects models and REML estimation.
• General Theory of Generalized Linear Models
Distributions. Link functions. Deviance. Common distributions. Overdispersion. Quasi-likelihood. Residuals.
• Binary Data
Analysis of binary data. Logistic regression.
• Other Distributions
Count data (Poisson distribution). Continuous non-negative data.
• Contingency Tables and Log-linear Models
Two-way tables: types of table and relevant models. Three-way tables.

Aims

• To review and extend the student's knowledge of the standard linear model.
• To introduce the more general ideas of Mixed Effects Models and Generalized Linear Models (GLM) by building on the familiar concepts of the linear model.
• To develop enough of the theory to allow a proper understanding of what these methods can achieve.
• To show how these methods are applied to data, and what kinds of conclusion are possible.

Learning outcomes

• understand the basic concepts.
• derive minor extensions and applications of the general theory.
• carry out straightforward regression analysis.
• assess the fit of a model to data, and make suggestions as to how to improve it if it is unsatisfactory.
• understand basic techniques of mixed effects modelling.
• carry out logistic regression and log-linear analysis of contingency tables.

Teaching methods

Lectures, with a complete set of printed notes, plus task and exercise sheets and 4 computer classes in semester 2.

36 lectures, no tutorials, 4 practicals

Assessment

One project in semester 2 (15% overall), and a three hour restricted open book examination (85%). Exam format: 5 questions from 6.

Full syllabus

Semester 1

• Review of simple linear regression. (2 sessions)
• General linear model; reduced models; replicates and lack of fit; weighted and generalized least-squares. (6 sessions)
• Diagnostics and model revision. Examination of residuals; types of residuals; influential observations; transformations. (3 sessions)
• More linear models and model-building. Use of the flexibility of the general linear model; strategy for model-building and variable selection. (7 sessions)
• Review. (2 sessions)
Semester 2
• Motivating examples. Review of linear model features, including indicator variables and aliasing. (2 sessions)
• Components of variance models. Equi-correlation model. REML estimation. (6 sessions)
• Introduction to generalised linear models; the exponential family, estimation of parameters. Deviance and inference. Deviances and the generalised linear model form of common distributions. Overdispersion. Quasi-likelihood. Residuals. (2 sessions)
• Analysis of binary data. Logistic regression. Odds. (2 sessions)
• Count data. Continuous non-negative data. (2 sessions)
• Contingency tables: introduction, distributions and connection with Poisson distribution with log link. Two-way tables: types of table and relevant models. Three-way tables. Ordinal categories. Equivalence of Multinomial analysis and logistic regression when there is a two-level factor dependent variable. Odds-ratios. (6 sessions)

Type Author(s) Title Library Blackwells Amazon
A Dobson, A.J. An Introduction to Generalized Linear Models Blackwells Amazon
B Christensen, R. Log-linear models and Logistic Regression Blackwells Amazon
C Atkinson, A.C. Plots, Transformations and Regression Blackwells Amazon
C Cook, R.D. \& Weisberg, S. Residuals and Influence in Regression Blackwells Amazon
C Draper, N. and Smith, H. Applied Regression Analysis Blackwells Amazon
C McCullagh, P J and Nelder, J A Generalised Linear Models Blackwells Amazon
C Montgomery, D.C. and Peck, E.A. Introduction to Linear Regression Analysis Blackwells Amazon
C Pinheiro, J.C. and Bates, D.M. Mixed-Effects Models in S and S-Plus Blackwells Amazon
C Seber, G.A.F. Linear Regression Analysis Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop on Mappin Street.

Timetable (semester 1)

 Wed 11:00 - 11:50 lecture Hicks Lecture Theatre A Thu 12:00 - 12:50 lecture Hicks Lecture Theatre A