775—Generalized Linear Models. [=BIOS 815] (3) (Prereq: STAT 713 or STAT 513, and STAT 705 or BIOS 757) Statistical theory and applications extending regression and analysis of variance to non-normal data. Encompasses logistic and other binary regressions, log-linear models, and gamma regression models.

Usually Offered: Irregularly

Purpose: To provide advanced students in statistics, biostatistics, and quantitative specialists in the physical and social sciences with a course of study in the theory and practice of modern extensions of the general linear statistical model.

Current Textbook: An Introduction to Generalized Linear Models, (2nd edition) by A.J. Dobson. Boca Raton, FL: Chapman & Hall/CRC, 2002.

 

Topics Covered	Chapters	Time
Review of the General Linear Model for Normal Data: Linear regression, fixed- and mixed-model ANOVA, Analysis of covariance	1.3, 2.1-2.2, 2.4	1.5 weeks
Extending the General Linear Model: Non-normal error structure, The exponential class, Linear and non-linear link functions	3.1-3.5	1 week
Theory of Estimation and Model Fitting: Likelihood functions and maximum likelihood, Iteratively reweighted least squares	4.1, 4.3-4.4	1 week
Theory of Statistical Inference: The deviance function, Analysis of deviance, Likelihood ratio tests, Wald tests, Confidence regions	5.1-5.7	2.5 weeks
Examples and Illustrations: Classical normal-based models, Logistic and other binary regression, Log-linear models for count data, Gamma regression models	6.3-6.5, 7.1-7.5, 9.1, 9.3-9.7	4.5 weeks
Extending Generalized Linear Models: Extending the exponential class, Overdispersed models, Quasi-likelihood models, Generalized estimating equations, Polytomous response models	Handouts	2.5 weeks

The above textbook and course outline should correspond to the most recent offering of the course by the Statistics Department. Please check the current course homepage or with the instructor for the course regulations, expectations, and operating procedures.  

Contact Faculty: John Grego