BIOS 345: Advanced Regression Analysis I (Linear Models and Generalized Linear Models)

Instructor

• Ben Saville, PhD, Assistant Professor of Biostatistics
• b [dot] saville [at] vanderbilt [dot] edu
• T-2316 MCN
• 615-343-3624

Course info

• Lectures: Tuesday and Thursday 10:00-11:30am, Light Hall
• Lab: Fri:11am-12pm, Light Hall
• Office hours: TBD
• Course webpage: http://www.vanderbilt.edu/oak/ (access to enrolled students only)

Textbooks

• Required
  • Rencher A.C., Schaalje, G.B, Linear Models in Statistics, Second Edition. John Wiley & Sons, 2008
• Optional
  • Dobson, A.J., Barnett A.G, An Introduction to Generalized Linear Models, Third Edition. Chapman & Hall/CRC 2008.
  • McCullagh P. and Nelder J.A. Generalized Linear Models, 2nd Edition. Chapman and Hall / CRC Monographs on Statistics and Applied Probability, 1989.
  • Searle, S.R. Linear Models John Wiley & Sons, 1971.

Course Objectives

Bios 345 and 346 will essentially consist of 3 modules: 1) theory of linear models; 2) generalized linear models; and 3) generalized linear models for clustered/longitudinal data. Bios 345 will cover the first module and a portion of the second module, with an emphasis on the underlying theory. Applications will be used to strengthen the student’s understanding of the theory. By the end of the course, the student should be able to do the following:

• Understand the theory of the classical linear model, including estimation and hypothesis testing in full rank and less than full-rank (ANOVA) models
• Understand how the theory relates to applications of the linear model
• Understand the theory and application of Bayesian linear models
• Understand the theory of the exponential family of distribution
• Understand the theory and application of generalized linear (regression) models, including logistic and poisson regression
• Understand Bayesian methods for generalized linear models and computational strategies for model fitting
• Formulate scientific questions involving continuous or categorical response data as regression problems

Course Outline

This course will cover the following topics:

• Matrix algebra review
• Multivariate normal distributions, non-central distributions, quadratic forms
• Linear model full rank estimation: Least squares, maximum likelihood, generalized least squares
• Linear model full rank inference: nested hypotheses, linear hypotheses, confidence intervals
• Linear model less than full rank models: estimation, hypothesis testing
• Sums of squares
• Bayesian linear model, Gibbs sampling
• Exponential family & generalized linear models (GLM)
• GLM estimation, inference
• Logistic & poisson regression

-- BenSaville - 04 Jan 2013