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Generalized linear models
12 September 2010
An Introduction to Generalized Linear Models
Geoff Vining
Virginia Tech
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.
Geoff Vining
Virginia Tech
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.