Introduction to Generalized Linear Models

This course provides an overview of generalized linear models, which extend the linear modelling framework to allow response variables that are not Normally distributed. The course is divided into three parts, each comprising a lecture session and a practical session using R.

The first part reviews the general linear model and considers its restrictions, motivating the development of generalized linear models (GLMs). An overview of the theory of GLMs is given, including estimation and inference. The part concludes with an introduction to fitting GLMs in R. The practical for this part considers the use of GLMs for continuous data, in particular comparing the log-Normal and Gamma models.

The second part focuses on the analysis of binary data. The lecture session begins by considering the exploration of binary data before introducing GLMs for binary data. Examples are given of both grouped and ungrouped binary data, providing case studies for model selection, model evaluation, interpretation, prediction and residual analysis. In the practical, two examples with a binary response are analysed using logistic regression.

GLMs are most commonly applied to binary or count data and the latter type of data is the focus of the final part. The analysis of rate data is considered first, introducing the concepts of offsets and overdispersion. Then an introduction is given to log-linear models for contingency tables. The practical covers both rate data and contingency table analysis using Poisson or quasi-Poisson models.

• Part I
• Part II
• Part II

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References

GLMs
An Introduction to Generalized Linear Models, 2nd Edition, A. Dobson. Chapman and Hall, 1990.
Generalized Linear Models. McCullagh, P. and J.A. Nelder. Chapman and Hall, 1989.
Statistical Theory and Modelling. D. V. Hinkley, N. Reid and E. J. Snell (eds). Chapman and Hall, 1990.

GLMs in R
An R and S-PLUS Companion to Applied Regression. J. Fox. Sage, 2002.
Modern Applied Statistics with S, Fourth Edition. W. N. Venables and B. D. Ripley. Springer, 2002.
Statistical Models in S. J. M. Chambers and T.J. Hastie (eds). Wadsworth, 1992.

Applications
Categorical Data Analysis, Second edition. Alan Agresti. Wiley, 2002.
Learning and practicing econometrics. W.E. Griffiths, R.C. Hill and G.G. Judge. Wiley, 1993.
Statistical Analysis and Data Display: An Intermediate Course with Examples in S-PLUS, R, and SAS. Heiberger, Richard M., Holland, Burt Springer, 2004.
Statistical modelling in GLIM. M. Aitkin, D. Anderson, B. Francis and J. Hinde. Clarendeon Press, 1989.

Last change: 2008-04-23 by rh