Student Seminar in Statistics

Topic: Mixed-Effects Models

Description:

Mixed-effects models play an increasingly important role in applied statistics. In this seminar, we discuss linear, nonlinear and generalized mixed-effects models emphasizing both theoretical foundations and issues in applications.

Prerequisites:

As prerequisites, we suggest (not enforced):

• Introductory course to probability and statistics
• Attended one advanced lecture in statistics (http://stat.ethz.ch/teaching/lectures)
• Basic knowledge of the software R (www.r-project.org)

Literature:

• Pinheiro, J. C. ; Bates, D. M.: Mixed-Effects Models in S and S-Plus. Springer, 2000 (Statistics and Computing)
• Jiang, Jiming: Linear and Generalized Linear Mixed Models and Their Application. Springer, 2007
• Demidenko, E.: Mixed Models, Theory and Applications. Wiley, 2004

Program:

Table of content and schedule.

Slides and Synopsis:

1. Motivation and Introduction (Slides, Synopsis)

2. The Linear Mixed-Effects Probability Model (Slides, Synopsis)

3. Optimization Algorithms (Synopsis)

4. Hypothesis Tests, Confidence Intervals (Slides, Synopsis)

5. LMMs in Practice (Slides, Synopsis)

6. Prediction of New Observations (Slides, Synopsis, R-Code 1, R-Code 2)

7. Introduction to Nonlinear Regression (Slides, Synopsis)

8. Nonlinear Mixed-Effects Models (Slides, Synopsis)

9. Fitting Nonlinear Mixed-Effects Models (Slides, Synopsis)

10. Introduction to Generalized Linear Models (Slides, Synopsis, R-Code)

11. Generalized Linear Mixed-Effects Models (Synopsis, R-Code)

Summary:

Some aspects of linear mixed models (Slides, R-Code).