Lecturer | Prof. Felix Abramovich (felix@math.tau.ac.il) |

Lecture Hours:
| Tuesday 16-19, Kaplun 319 |

- Introduction
- Standard (normal) linear regression model
- Generalized linear regression model

- Theory of Generalized Linear Models
- Model components
- exponential family and its properties
- link functions

- Maximum likelihood estimation
- Newton-Raphson method
- iteratively reweighted least squares

- Goodness-of-fit
- analysis of deviance
- Pearson statistic
- analysis of residuals

- Model selection

- Model components
- Particular Models
- Binary data
- Binomial data
- Multinomial data
- Poisson data

- Overdispersion & Quasi-Likelihood Models
- Nonparametric GLM
- Normal linear models with heterogeneous variance and GLM
- Generalized linear mixed effects models

- Dobson, A.J. An Introduction to Generalized Linear Models.
- McCullagh, P. and Nelder, J.A. Generalized Linear Models.
- Wood, S.N. Generalized Additive Models. An Introduction with R (Chapter 2).
- Myers, R.H. and Montgomery, D.C. A tutorial on Generalized Linear Models.
*Journal of Quality Technology*,**29**, 274-291. - Chapter 5: Green, P.G. and Silverman B.W. Nonparametric Regression and Generalized Linear Models.

- Aitkin, M., Francis, B., Hinde, J. and Darnell, R. Statistical Modelling in R.
- Faraway, J.J. Extending the Linear Models with R (Chapters 1-10).
- Venables, W.N. and Ripley, B.D. Modern Applied Statistics with S (Chapter 7).

In addition, you can enjoy various R packages that are not included in ka standard R software. For example, you can find very useful Ripley's software provided with the book "Modern Applied Statistics with S". To use Ripley's software enter S-Plus and give the command:

- To fit a generalized linear model you will generally use the function
**glm**:- >glm(formula, family=...(link=...),...)
- The
**glm**function creates an object of class glm that contains most of information you need. See**help(glm.object)**for details.- For some data the convergence of the iteratively reweighted least squares algorithm is slow and does not occur in (default) 10 iterations. It may happen, for example, in binomial models with a lot of empty cells. R gives you a "Warning". Don't panic! You can increase the number of iterations by the parameter
*maxit*:- >glm(formula,...,maxit=...)
- To evaluate the fitted model at some new values of the predictors use the function
**predict**:- >predict(glm.object, type=...,se=T)
- The output will contain, in particlular, a vector of estimated response (depending on
*type*) and a vector of standard errors for constructing confidence intervals for the mean response.