Generalized Linear Mixed Models

Theory and data analysis methods for Generalized Linear Mixed Models (GLMM), extending regression to exponential families and random effects.

Course Goals and Overview

This course covers the theory and data analysis methods of Generalized Linear Mixed Models (GLMM). GLMM is fundamentally an extension of regression analysis:

  1. Response Variable Extension: Extends from normal distribution to distributions in the exponential family.
    • Binomial distribution $\rightarrow$ Logistic regression
    • Poisson distribution $\rightarrow$ Poisson regression
  2. Predictor Variable Extension: Extends to include not only fixed effects but also random effects.

Through these extensions, students will study Covariance Pattern Models and Random Coefficient Models (Hierarchical Models), and learn how to analyze Longitudinal Data.

Prerequisites

Enrollment is restricted to students who have completed the following prerequisite courses. Verification of grades in the first class is required.

  1. Undergraduate Mathematical Statistics II or Graduate Mathematical Statistics
  2. Undergraduate Regression Analysis or Graduate Linear Models

Course Operation

  • 2 Hours: Pre-recorded video lectures uploaded to RunUs. Students can watch at their convenience.
  • 1 Hour: Real-time interaction with students via Zoom.
  • Focus: Lectures will be based on the instructor’s notes. The course will focus on case studies analyzing various models using SAS.

Instructor Information

  • Instructor: Prof. Seung-Ho Kang

Topics

  • One-way classifications
  • Single-predictor regression
  • Linear models
  • Generalized linear models
  • Linear mixed models
  • Generalized linear mixed models
  • Models for longitudinal data

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