STAT 741: LINEAR MODELS II

COURSE OUTLINE, SPRING 2022

Required Textbooks:

Agresti, A. (2015), Foundations of Linear and Generalized Linear Models. New York: Springer.

Faraway, J. J. Linear Models in R. (2nd ed., 2015) Boca Raton, FL: Chapman & Hall/CRC.

Faraway, J. J. Extending the Linear Model with R. (2nd ed., 2016) Boca Raton, FL: Chapman & Hall/CRC.

Recommended Textbook:

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

Instructor: Paul J. Smith, Statistics Program

Office hours: MWF 1-2, by appointment using Zoom.

E-mail: pjs@umd.edu

Schedule: Spring 2022, MWF 2.

Prerequisites: STAT 740 or consent of instructor.

Course Description: 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 R statistical computing package.

Topics:

Topics in Complex Designs: Blocking and randomization. Unbalanced and incomplete designs. Latin squares, balanced incomplete block designs, and generalizations. Complete factorial designs, fractional factorial designs at two levels, graphical methods.

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 software.

Generalized Linear Models: GLM assumptions, logistic regression and loglinear models for frequency data. Methods of estimation, including maximum likelihood and generalized estimating equations.

Nonparametric Regression: Kernel methods, splines, local linear regression, additive models. Regression trees (Note: these topics will only be covered as time permits.)

Exams and Grading:

Midterm: Friday, March 18 (tentatively). (Click here for practice problems).

Final: Monday, 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. Homework assignments will be posted on ELMS.

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.

Clarke, B. R. (2008), Linear Models. New York: J. Wiley.

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.

Monahan, J. F. (2008). A Primer on Linear Models. Boca Raton, FL: Chapman & Hall/CRC.

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

Rencher, A. C. and Schaalje, G. B. (2008). Linear Models in Statistics (2nd ed.). 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.

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