R Programming for Actuarial Science

27 Generalised Linear Models: Poisson Regression

Peter McQuire

library(dplyr)

27.1 Introduction

The aim of this chapter is to provide an introduction to this important topic by considering:

• what is a Generalised Linear Model (“GLM”);
• the aims of GLMs and what sort of problems can be solved using GLMs;
• the issues encountered when using GLMs.

Rather than cover several versions of GLMs in what is a relatively short chapter, we concentrate on one particular type – Poisson Regression. This is often the model of choice of insurance companies when modelling claim frequencies. We will look at several examples by analysing various datasets; in this way the reader should develop an understanding of the fundamentals of GLMs, and their benefits.

The datasets used in this chapter to which we fit GLMs incorporate data which has been simulated using specific equations, the code for which is included on the website; the reader then has the facility to alter the data to understand the effect such changes have on the model output.

There are numerous excellent books on Multiple Regression and GLMs; please see the Recommended Reading. It is beyond the scope of this book to cover the range of models in any great detail. In particular, the reader is encouraged to study various other types of GLMs such as logistic and probit models which are not covered in this chapter.

27.2 Examples/Exercises/Data

There are four datasets utilised in this chapter. Data1 is artificially simple in that all lives ...