## MAS31001 Generalised Linear Models

Semester 2, 2022/23 | 10 Credits | ||||

Lecturer: | Dr Kostas Triantafyllopoulos | Reading List | |||

Aims | Outcomes | Teaching Methods | Assessment | Full Syllabus |

This module introduces the theory and application of generalised linear models. Such models can be used for modelling binary or count data, where the dependent variable is not normally distributed; this increases substantially the range of problems that can be studied. The general theory will be presented, in which the ordinary linear model is a special case. Mixed effects models will also be discussed. Application of the methods will be demonstrated using R, including the use of exploratory data analysis methods as a precursor to modelling.

**Prerequisites:** MAS223 (Statistical Inference and Modelling)

No other modules have this module as a prerequisite.

## Outline syllabus

- Introducing GLMs: theoretical concepts;
- binomial, ordinal, multinomial and Poisson regression;
- incorporating mixed effects in linear and generalised linear models;
- implementation with R.

## Aims

- introduce the theory of generalised linear models, including the use of random effects;
- show how these models are applied to data, and what kinds of conclusions are possible;
- demonstrate how generalised linear models can be fitted to data using R;

## Learning outcomes

- describe the mathematical framework that underpins generalised linear modelling;
- identify circumstances in which generalised linear models can be used for data analysis, incorporating random effects as necessary;
- fit generalised linear models using R, and interpret the output;
- conduct an exploratory data analysis and interpret the results in the context of fitting a generalised linear model;

## Teaching methods

There will be formal lectures, which will involve the explanation of theoretical concepts and their application to worked examples. The motivation, rationale, advantages and disadvantages of the various methods taught will be discussed as appropriate. Detailed lecture notes will be provided, which students will be expected to study in their own time to assimilate the material. Lectures will include practical demonstrations of analysis using R. Students will work through set exercises in both theory and R implementation, and submit homework for marking, although this will not be part of the formal assessment.

20 lectures, no tutorials

## Assessment

One formal 2 hour written examination. All questions compulsory.

## Full syllabus

- Introduction to GLMs: link functions, GLM distributions and assumptions, distributional properties.
- Fitting GLMs: the likelihood, implementation in R
- Model fit and variable selection: deviance, Pearson X2, comparing nested models, residuals, estimation of dispersion parameter.
- Binomial, ordinal and multinomial logistic regression: link functions, model building, odds ratios, examples.
- Poisson regression: modelling of counts; contingency tables as Poisson regression.
- Over-dispersion: quasi-likelihood, quasibinomial, quasi-Poisson. Examples where the dispersion parameter is estimated.
- Penalised likelihood and AIC for both GLMs and normal theory linear models; step- wise selection.
- Mixed effects for correlated observations; incorporating mixed effects in linear and generalised linear models; implementation in R.

## Reading list

Type | Author(s) | Title | Library | Blackwells | Amazon |
---|---|---|---|---|---|

B |
Faraway | Extending the linear model with R: Generalized linear, Mixed Effects and Nonparametric Regression models (Second edition) | Available online | Blackwells | Amazon |

(

**A**= essential,

**B**= recommended,

**C**= background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.