## MAS367 Linear and Generalised Linear Models

 Semester 1, 2019/20 10 Credits Lecturer: Dr Jonathan Jordan uses MOLE Timetable Reading List Aims Outcomes Assessment

The module will further develop the general theory of linear models, building on theory taught in MAS223. Extensions from the L2 course will include methods for dealing with large numbers of independent variables. The module will also introduce generalised linear models, which can be used for modelling data such as binary data and count data, where a normal distribution would not be appropriate. These developments dramatically extend the range of problems that can be studied. The methods will be implemented using R.

Prerequisites: MAS223 (Statistical Inference and Modelling)

The following modules have this module as a prerequisite:

 MAS370 Sampling Theory and Design of Experiments MAS474 Extended Linear Models

## Outline syllabus

• Review of Linear Regression: Simple and multiple linear regression, linear model in matrix form, LS estimators and its distributions.
• General hypothesis testing: Distribution of LS estimators, confidence intervals, the general hypothesis testing, ANOVA tables.
• Transformations and variable selection: Variance stabilization transformations, Box-Cox transformations, variable selection, automated methods for variable selection.
• Introduction to generalized linear models: Introduction, definition, GLM distributions.
• GLM estimation: Parameter estimation, use of deviance in GLMs to test model fit. Model building (analysis of deviance), types of residuals, quasi likelihood.
• Binary response: Likelihood, links, examples, odds ratio, logistic regression.
• Poisson regression: Poisson regression for count data, using offsets to adjust for exposure.
• Two way contingency tables: Response & controlled variables, association and homogeneity, probability distributions for two-way tables.

## Aims

• To review and extend the students knowledge of the standard linear model, building on concepts introduced at L2.
• To introduce the theory of generalised linear models.
• To show how these methods are applied to data, and what kinds of conclusions are possible.
• To demonstrate the fitting and interpretation of linear and generalised linear models to data using the statistical computing language R.

## Learning outcomes

• Obtain a technical understanding and appreciation of ordinary and generalised linear modelling methods.
• Be able to identify circumstances in which ordinary and generalised linear models can be used for data analysis, and understand what conclusions and inferences can be drawn.
• Know how to fit linear and generalised linear models using R, and interpret the output

20 lectures, no tutorials

## Assessment

One formal 2 hour open-book written examination. Format: 3 compulsory questions.