Generalised Linear Models

Module code: MA7021

This module extends the ideas used in linear modelling to a more general framework, which allows the possibility to include a number of analyses in one general approach. This occurs when the response variable is dependent, through some link function, on the predictor of an unknown linear combination of explanatory variables and an error random variable. By choosing an appropriate link function and error structure, many data analysis techniques can be covered within a general framework: log-linear modelling for analysing counts and proportions, linear Poisson regression modelling of continuous variables, and linear logistic regression modelling for binary data. The two main objectives of analysis using these models include determining which explanatory variables are important, and the exact relationship of these variables to the response variable. It is possible to associate confidence intervals with estimates or predictions obtained from the model and assign p-values to the hypotheses you want to test. The model analysis is based on deviance, which offers a method for assessing the acceptability of any proposed model. Illustrations of how to use statistical software package R to analyse data using generalised linear models are given.