Linear Models and GLM: Spring 2010

Quiz 2 Solutions (Rnw source)

Assignment 3 Solutions (Rnw source)

Quiz 2 (7 April, 2010)

Assignment 3 (10 March, 2010)

Assignment 2 (updated) (13 February, 2010)

R mini-course

Assignment 1 (8 January, 2010)

Course Information

Instructor: Deepayan Sarkar <deepayan.sarkar@gmail.com>
Schedule: Mon Wed Fri 11:45 - 12:45, Thu 14:00 - 15:00 (Tutorial); January 4 - April 16, 2010 (Room 23).
Office hours: Tue 14:00 - 15:00, Room 213 Faculty Building, or by appointment

Outline (tentative)

Linear statistical models
Examples of linear models:

One-sample problem
Simple linear regression
One-way classification
Two-way nested model
Two-way crossed model without and with interactions
Nested classification model
Multiple regression

Gauss-Markov model
Normal equations and least square estimation, estimable linear functions, g-inverse and solution of normal equations. Best Linear Unbiased Estimates (BLUEs).
Gauss-Markov Theorem
Variances and covariances of BLUEs
Normality assumption of error. Maximum likelihood estimation vs Least square estimation/MLE vs BLUE. MVUE vs BLUE.
Estimation of error variance. Degrees of freedom.
Fisher-Cochran theorems, distribution of quadratic forms.
Multiple comparisons
Analysis of Covariance (ANCOVA)
Random effects and mixed models
Generalized Linear Models (GLMs), Logistic regression, Log-Linear Models.
Practical applications using the R statistical software environment.

Prerequisites

Linear Algebra
Methods of Statistical Inference - I

References

Plane Answers to Complex Questions by R. Christensen.
Linear Statistical Inference by C. R. Rao.
Log-Linear Models by R. Christensen.
Generalized Linear Models by P. McCullagh and J. A. Nelder.

Grading

Assignments: 15%
Quizzes: 10%
Mid-term Exam: 25%
End-term Exam: 50%

Assignment policy (tentative)

Homework assignments will be handed out roughly once every two weeks.

Assignments should not be submitted. Instead, students will be randomly selected (using simple random sampling with replacement) and asked to present their solutions during tutorial sessions. Grades will be given based on the presentations. Students who are called upon but are not present will lose points for that particular day.

Depending on progress, some of the later assignments may be small projects specifically assigned to certain students or groups of students.

Quizzes

There will be two surprise (unscheduled) quizzes given in the class over the course of the semester. No supplementary quiz will given for students who miss a quiz.

Software

Students will be expected to learn the statistical software R and use it for practical assignments. Some of the tutorial sessions will be used to teach R as necessary during the course. Information on R is available from the CRAN website or one of its mirrors (the US mirror is usually more responsive).