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Two-day Short course: An Introduction to Generalized Linear Models Teacher: Geoff Vining Professor of Statistics, Virginia Tech http://www.stat.vt.edu/facstaff/ggvining.html Period: June 14-15 2011 Location Department of Statistics – University of Milano Bicocca, Edificio U7 Via Bicocca degli Arcimboldi, 8 - 20126 Milano. Map Audience: The course will be directed to phd students in statistics and related fields and it will be also opened, free of charge, to research fellows, post doctoral students, researchers of the Departments supporting the initiative. A number of places (max 10) will be opened to people form outside academic institutions. A fee of 150 euros will be applied in this case. Program. Generalized Linear Models (GLM) is an important analysis tool for data well modeled by a large number of families of distributions. Specifically, GLM uses maximum likelihood estimation for any member of the exponential family of distributions. Ordinary least squares estimation for normally distributed data, logistic regression for binomial data, and Poisson regression are all special cases of GLM. This course assumes some basic familiarity with ordinary least squares estimation. This course is based on the newly released Myers, Montgomery, Vining, and Robinson (2011) Generalized Linear Models, 2nd ed. (Wiley). It starts with a review of multiple linear regression analysis with a focus on weighted least squares. It then provides an introduction to logistic regression, emphasizing the use of maximum likelihood estimation. The course next discusses Poisson regression. It then generalizes maximum likelihood estimation to any member of the exponential family, with particular emphasis on the gamma distribution. It concludes with a brief overview of generalized linear mixed models. The course discusses such issues as residual analysis within GLM, choice of link function, and over-dispersion. Examples illustrate each methodology. The course uses both SAS’s PROC GENMOD and R. The instructor will provide course notes. Students are encouraged to bring copies of the book with them. Topics 1st day 1. Overview of the Course 2. Review of Ordinary Least Squares a. Model and Assumptions b. Least Squares Estimation c. Maximum Likelihood Estimation d. Testing 3. Generalized or Weighted Least Squares a. Weights Known b. Variance-Covariance Matrix Known Apart from a Constant 4. Logistic Regression 5. Basics of Generalized Linear Models a. Exponential Family b. Linear Predictors and Link Functions c. Estimation 2nd day 1. Review of Day 1 2. Basics of Generalized Linear Models – Continued a. Testing and Deviance b. Residual Analysis c. Using Software 3. Introduction to Linear Mixed Models 4. Introduction to Generalized Linear Mixed Models Reference Myers RH, Montgomery DC, Vining GG, Robinson TJ. (2010). Generalized Linear Models with Applications in Engineering and the Sciences Wiley Series in Probability and Statistics Language the course will be held in English Contacts For any enquiries please contact Riccardo Borgoni Department of Statistics, University of Milano Bicocca E-mail [email protected]
