STATISTICS 538 (2010-2011, Term 1)

GENERALIZED LINEAR MODELS (1.5 Credits)

Lectures: Mon. and Wed. 9:30-11:00, LSK 301, from October 25 to December 1.

Instructor: Paul Gustafson, LSK 326, gustaf at stat dot ubc dot ca.
Office hours: Wed 12-1 (picked to not conflict with other courses in the department - I should have reasonably good availability at other times as well).

Prerequisites: Open to any interested graduate students in the Department of Statistics. Graduate students from other departments are welcome, provided they have sufficient statistical and mathematical backgrounds. Such students should consult the instructor about suitability.

Description: Generalized Linear Models (GLMs) extend much of the `niceness' of linear models to situations where the response variable is not continuous. Consequently these models are popular for analysis in the common scenarios of response variables which are binary, categorical, counts, proportions, or directions. GLMs have become a big part of the `statistical toolbox' in most application areas. This course will be a core introduction to GLMs, including a quick review of linear models, the fundamental formulation of GLMs, discussion of link functions, iterative least-squares algorithms, deviance and asymptotic theory, residuals, quasi-likelihood, and quadratic variance functions. A wide range of GLM applications will be discussed.

Coursework: Will include a mix of data-analytic and empirical exercises (i.e., using the computer) and more theoretical exercises. Students will develop (or already have) some computing skills with the R software package.

Here will be the PROBLEMS to work on. The list will be added to as the course progresses. I envision the first batch due roughly four weeks into the course, and the second batch due about a week into the exam period.

Website (this page): www.stat.ubc.ca/~gustaf/stat538.html

Textbook: Extending the linear model with R: generalized linear, mixed effects, and nonparametric regression models, Julian Faraway. Chapman and Hall / CRC Press, 2006 Note added Sept. 13th. Earlier I put in a bookstore order for hardcopies. Today I found out that there is electronic access for the UBC community via UBC library -> "MyiLibrary," though you may find readability issues with this online version.

Other References:

An Introduction to Generalized Linear Models, Second Edition, by Annette J. Dobson. Chapman and Hall / CRC Press, 2001 (Freely available to UBC community via library subscription to StatNetBase.)

Generalized Linear Models, Second Edition. McCullagh and Nelder. Chapman and Hall / CRC Press, 1989.

Modern Applied Statistics with S. Venables and Ripley. Springer, 2002.

Lecture notes: I plan to bring in rough/incomplete slides (which I'll post in advance), and then we will fill in details in-class.

Very tentative lecture plan (aka GLMs in twelve easy steps!):

Review of linear models: nice features, limitations. [skeletal notes (pdf)].

Introduction to logistic regression. [skeletal notes (pdf)].

The generality of GLM I: link, variance function, fitting procedures [skeletal notes (pdf)].

Modelling count data - Poisson regression. [skeletal notes (pdf)].

The generality of GLM II: deviance. [skeletal notes (pdf)]

Overdispersion, quasi-likelihood. [skeletal notes (pdf)].

Model selection. [skeletal notes(pdf)]. Also, R code implementing the examples: stepwise.R, crossval.R.

Modelling categorical data: nominal multinomial regression [skeletal notes (pdf)].

Modelling categorical data: ordinal multinomial regression. [skeletal notes (pdf)].

Contingency tables I. [skeletal notes (pdf)].

Contingency tables II. [skeletal notes (pdf)].

From GLM to GAM: lines to curves. [skeletal notes (pdf)].

Scribbled slides: I had a request to post the post-lecture (i.e., marked-up) versions of the slides, so I'll put these here.