Math 4392: Advanced Linear Models - Spring 2016

Instructor: Jimin Ding; 

Office: Cupples I, Room 112A;
Email: jmding@math.wustl.edu
TA/Grader: Liqun Yu (yuliqun@math.wustl.edu)

Office Hours: Wed. 1-3pm. or by appointment.

Topics covered:

Review of basic linear models relevant for the course; generalized linear models including logistic and Poisson regression (heterogeneous variance structure, quasilikelihood); linear mixed-effects models (estimation of variance components, maximum likelihood estimation, restricted maximum likelihood, generalized estimating equations), generalized linear mixed-effects models for discrete data, models for longitudinal data, optional multivariate models as time permits.


The computer software R will be used for examples and homework problems. Implementation in SAS will be mentioned for several specialized models.

We will also add some in-class real-life consulting to apply the models learned in class.

Prerequisites:

Math 439 (or instructor's consent) and a course in linear algebra, such as Math 309 or 429.

Textbook:

C.E. McCulloch, S.R. Searle, J. M. Neuhaus,
Generalized, Linear and Mixed Models, , 2nd ed.
John Wiley & Sons, 2008.
 
J. Faraway,
Extending the Linear Model with R : Generalized Linear, Mixed Effects and Nonparametric Regression Models ,
Chapman & Hall/CRC, 2005.
Book Website


Remarks:


• Review of basic linear models will be taught together with Chapter 1-3 as an introduction.
• We will cover selected topics from Chapters 5-10. Detailed schedule will be updated periodically on the course website.
• This 2nd edition of the textbook is different from the 1st edition. The major changes are in Chapter 8, which contains the old Chapter 7 and expands to non-normally distributed outcomes, and Chapter 9, which extracts and expands coverage of marginal versus conditional models. (Chapter 10 and 12 are two new chapters on multivariate models and robustness discussions.) Our homework assignments will be based on the 2nd edition.

Reference Books:

• W.W. Stroup, Generalized Linear Mixed Models: Modern Concepts, Methods and Applications, Chapman & Hall/CRC, 2012.
  
• J. Jiang, Springer, Linear and Generalized Linear Mixed Models and Their Applications, 2010.
  
• G. Verbeke and G. Molenberghs, Springer, Linear Mixed Models for Longitudinal Data, 2000.
  

Exams and Homeworks:

There will be one in-class midterm on March 9 (Wed.) and a final exam on May 11 (Wed.), 11:30-2:30pm. You may take no more than 1 page (letter size, double-sided) sheet for the midterm and 2 pages for the final exam.

There will be one in-class presentation and homework sets every other week. Homework will be collected on Monday in class. Late homework will only be accepted within 48 hours of due time and the grade will be scaled by 70% as a penalty. Make a copy of each homework before you hand it in !! It may not be returned before you need to refer to it for the next homework (or for the next test).

Collaboration:

Collaboration on homework is allowed and can be helpful (and fun). However, you must do all written work by yourself, both answers to homework questions and computer programs. If you collaborate with someone on a homework, list his or her name in a note at the top of the first part of your homework. There should be NO COLLABORATION on exams. Following "the academic integrity policy", acamedic misconducts and dishonesty will be reported to the university academic integrity office and seriously affect the grade.

Grades:

Your grade will be based on the in-class presentation, the in-class midterm and the final exam, together with homeworks in the proportions. Then your final letter grade is determined as follows. The A range will be 85 to 100, the B range will be 70 to 85, the C range will be 60 to 70, and the D range will be 50 to 60, with plus and minus grades given to the top 10% and bottom 10% students in each of these ranges. (If you elect ``Credit/No Credit'', Cr means D or better.)

Homework	40%
Presentation	15%
Midterm exams	20%
Final exam	25%

Good books for reviewing elementary statistics:

• A Data-Based Approach to Statistics,R. L. Iman, Duxbury Press, 1994.
  
• Statistics and Data Analysis from Elementary to Intermediate, A. J. Tamhane and D. D. Dunlop, Prentice-Hall, 2000.
  
• Design and analysis of experiments, 2nd ed., Douglas Montgomery, John Wiley & Sons, 1984. (Good for multiple-comparison procedures.)
  
• Applied Linear Statistical Models, 4th ed., John Neter, M. Kutner, C. J. Nachtsheim, and W. Wasserman, Irwin/McGraw Hill, 1999.
  
• Applied Multivariate Statistical Analysis. 5th ed., R. A. Johnson and D. W. Wichern, Prentice Hall, 2002.