Course Description
Extension of linear models to data with heterogeneous variance and correlated repeated measures. Mixed effects, log-linear, and generalized linear models are considered. Statistical inference is carried out using quasi-likelihood, conditional likelihood, marginal likelihood, and generalized estimating equations. Applications in public health and biomedical research.
Athena Title
LINEAR AND GLM
Prerequisite
BIOS 8010
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
A student completing this course should be able to: 1. Describe mixed effects, log-linear and generalized linear models. 2. Describe various approaches to model fitting including maximum likelihood, conditional likelihood, marginal likelihood, quasi-likelihood, and generalized estimating equations. 3. Describe the inferential properties of parameter estimators. 4. Fit linear and generalized linear models using statistical software. 5. Apply linear and generalized linear models to public health and biomedical data.
Topical Outline
1. Background for generalized linear models a. Linear models and likelihood theory b. Exponential family of distributions c. Motivation: Why more than linear regression 2. Introduction to generalized linear models a. Formulation / Link functions b. Maximum likelihood estimation and inference c. Deviance 3. Generalized linear models for correlated continuous data a. Models and estimation b. Linear mixed models c. Longitudinal data analysis 4. Analysis of discrete and counts data a. Logistic regression, probit regression, complimentary log-log models b. Poisson regression, negative binomial regression c. Log-linear models 5. Correlated discrete data a. Marginal and conditional models b. Generalized linear mixed models (GLMMs) c. Conditional likelihoods for GLMMs d. Overdispersion 6. Model diagnostics a. Diagnostic measures b. Local influence analysis c. Goodness-of-fit statistics 7. Generalized estimating equations a. Estimating functions b. Quasi-likelihood c. Generalized estimating equations
Syllabus
Public CV