Description

Generalized linear models (GLMs) are used to represent the relation between a response variable and a set of "covariates" using a mathematical expression involving unknown parameters entering linearly in the relation. For the response variable, the GLM supports a wide range of scenarios such as binary data, count data, waiting times, and of course also Gaussian data, in which case one has the usual linear model (LM).

Generalized Additive models (GAMs) are an appealing extension of the GLM for situations where the assumption of covariates entering linearly into the linear predictor is too restrictive. Such situations are likely to occur in the natural, environmental, and medical sciences, to name a few, since most natural processes possess an intrinsically nonlinear character, which shows linear behavior only over small ranges of the predictor variables. More specifically, a generalized additive model is of the shape

E(y|x₁,..., x_p) = h(f₁(x₁)+....+ f_p(x_p))

where f₁,..., f_p are smooth unspecified (!) functions, as opposed to the linear terms used in the generalized linear model. In this project you will get some insight into the methodology of generalized additive model fitting. Specifically, you will study the principles behind the "smoothers", which estimate the functions f_j, and will investigate how they are integrated into the generalized linear model framework. You will apply these techniques on real data sets, which you are welcome to choose according to your field of interest, using the statistical programming language R.

Prerequisites

The project would be ideal for those who have also attended Topics in Statistics III/IV in 2010/11, though this is not a formal prerequisite, and the project is also possible for students who have not attended this lecture.

Resources

• Fahrmeir, L, and Tutz, G. (2001) Multivariate Statistical Modelling Based on Generalized Linear Models, Springer.
• Ruppert, Wand and Carroll (2003), Semiparametric regression, Cambridge University Press.
• Bowman, A.W. and Azzalini, A. (1997), Applied Smoothing Techniques for Data Analysis , Oxford Statistical Science Series.
• Hastie, H. and Tibshirani, R.J. (1990), Generalized Additive Models , Chapman and Hall.
• A nice tutorial on GAMs.