Lectures notes for MATH3091, Statistical Modelling II

Preface

The pre-requisite module MATH2010: Statistical Modelling I covered in detail the theory of linear regression models, where explanatory variables are used to explain the variation in a response variable, which is assumed to be normally distributed.

However, in many practical situations the data are not appropriate for such analysis. For example, the response variable may be binary, and interest may be focused on assessing the dependence of the probability of ‘success’ on potential explanatory variables. Alternatively, the response variable may be a count of events, and we may wish to infer how the rate at which events occur depends on explanatory variables. Such techniques are important in many disciplines such as finance, biology, social sciences and medicine.

The aim of this module is to cover the theory and application of what are known as generalised linear models (GLMs). This is an extremely broad class of statistical models, which incorporates the linear regression models studied in MATH2010, but also allows binary and count response data to be modelled coherently.

These notes are based on material written by previous lecturers of this course, including Sujit Sahu, Dave Woods and Chao Zheng.