Instructor: Paul J. Smith, Statistics Program

Office hours:  MW 1-2, MTH 4404
Telephone:  (301) 405-5012 or (301) 405-2327
E-mail:  pjs@math.umd.edu

Prerequisites:  STAT 740 or consent of instructor.

STAT 741 is the second semester of a year-long sequence STAT 740-741 dealing with analysis of linear models, least squares and related topics.  This course deals with complex analysis of variance models, random and mixed effects models, and generalized linear models for discrete response variables.  Material from STAT 740-741 is part of the Graduate Written Examination in Applied Statistics.

This course will deal with both applied and theoretical topics. Data analysis and interpretation are essential components of the course, and students will analyze real world data sets using the SAS statistical computing package.

Topics:

• Analysis of Complex Designs:  Complete and incomplete layouts, Latin squares, balanced incomplete block designs, and generalizations.  Complete factorial designs, fractional factorial designs at two levels, graphical methods.  Crossed and nested factors in higher order layouts.
• Random Effects:   Definitions, ANOVA estimates in balanced models, distribution theory.  Unbalanced random effect designs, maximum likelihood (ML) and restricted maximum likelihood (REML) estimates.
• Mixed Models:  Balanced designs, ANOVA estimates and tests, multivariate formulation and tests.  Split-plot and repeated measures designs.  Unbalanced mixed models, ANOVA estimates, ML and REML estimates, computational algorithms, use of SAS.
• Generalized Linear Models:  GLM assumptions, logistic regression and loglinear models for frequency data.  Methods of estimation, including maximum likelihood and generalized estimating equations. Random effects and GLMM.
• Nonlinear Regression:  Nonlinear least squares, computational issues, examples. (Note: this topic will only be covered if time permits.)

Exams and Grading:

Midterm: Friday, March 16 (click here for practice problems).

Final: Wednesday, May 16, 1:30-3:30 p.m.

Homework: Frequent problem sets will be assigned. These will be a mix of theoretical and applied problems involving analysis of real data sets on the computer. Click here for homework assignments.

Grading: The midterm and final will each count for approximately 20% of the grade and the homework will count for approximately 60%.

References:

Christensen, R. (2002), Plane Answers to Complex Questions: The Theory of Linear Models (3rd ed.). New York: Springer.

Cody, R. P. and Smith, J. K. (1997).  Applied Statistics and the SAS Programming Language.  Upper Saddle  River, NJ: Prentice-Hall.

Hocking, R. (1996).   Methods and Applications of Linear Models.  New York: J. Wiley.

McCullagh, P. and Nelder, J. A. (1989).   Generalized Linear Models (2nd ed).  New York: Chapman and Hall.

Milliken, G. and Johnson, D. (1984).  Analysis of Messy Data, Vol. I: Designed Experiments.  New York: Van Nostrand-Reinhold.

Rao, P. S. R. S. (1997).  Variance Components Estimation.   New York: Chapman & Hall.

Scheffe, H. (1958).  The Analysis of Variance.  New York: J. Wiley.

Searle, S. R., Casella, G. and McCulloch, C. E. (1992).   Variance Components.  New York: J. Wiley.

Stapleton, J. (2009). Linear Statistical Models.  (2nd ed.)  New York: J. Wiley.