Introduction to Generalized Linear Modelling

Preliminary statement. When I first wrote my lecture notes for the Part II course, Sarah Shea– Simonds very kindly typed the core notes in TeX, and I added to them bit by bit, again in TeX. However, my style was still rather like a telegram, partly as I was trying to save on paper. Now that I am retired, I have time to retype the notes in LaTeX. I have tried to make the style rather more ‘flowing’, and have included more various graphs, exercises, Tripos questions and solutions. This editing process is quite enjoyable but rather slow. I’ll put the revisions on my webpage from time to time, and of course would appreciate comments and suggestions. Special thanks are due to Professor Yuri Suhov for his comments and suggestions. There are already several excellent books on this topic. For example McCullagh and Nelder(1989) have written the classic research monograph, and Aitkin et al. (1989) have an invaluable introduction to the pioneering software GLIM. Although I was very glad to learn a great deal by using GLIM, that particular software was superseded some years ago by excellent and powerful languages such as S-Plus and R. Students will naturally gain a much deeper understanding of the theory by putting it into practice on real (if small) datasets. An excellent text book to help them to do this in Splus and/or R is the one by Venables and Ripley (2002), particularly their Chapters 6 and 7. Dobson (1990) has written a very full and clear introduction, which is not linked to any one particular software package. Agresti (2002) in a very clearly written text with many interesting data-sets, introduces Generalized Linear Modelling with particular reference to categorical data analysis. The notes presented here are designed as a SHORT course for mathematically able students, typically third-year undergraduates at a UK university, studying for a degree in mathematics or mathematics with statistics. The text is designed to cover a total of about 20 student contact hours, of which 10 hours would be lectures, 6 hours would be computer practicals, and the remaining 4 are classes or small-group tutorials doing the problem sheets, for which the solutions are available at the end of the book. It is assumed that the students have already had an introductory course on statistics. While my notes are not dependent on any one particular statistical software, I wrote ‘worksheets’ to serve as computer practicals to introduce the students to (S-plus or) R. These worksheets (now extended somewhat) may be seen on