ST 762, FALL 2009Nonlinear Models for Univariate and Multivariate ResponseInstructor: Marie Davidian, Professor, 5124 SAS Hall, 515-1940, [email protected] meeting: TTh 1:30–2:45 pm, SAS Hall 2229Instructor’s office hours: T 12:00–1:00 pm, in SAS Hall 5214 or Cox 308Course Description: This course will provide a detailed treatment of regression models and asso-ciated inferential m ethods both for univariate and multivariate (e.g. repeated measures) response.The techniques to be discussed are now an essential part of the modern statistician’s toolkit andare widely used in numerous application areas.The first 1/2 to 2/3 of the course will focus on nonlinear regression models for univariate re-sponse, including models for nonconstant response variance. The r emaind er of the course willbe devoted to introduction to extension of the univariate model to two popular typ es of nonlin-ear regression models for multivariate response: (i) “population-averaged” models and models forcovariance structure will discus sed; methods for fitting these models are popularly known in theliterature as “generalized estimating equations,” and (ii) “subject-specific” models, e.g., generalizedlinear and nonlinear mixed effects models.Properties of competing inferential tech niques and the effects of model misspecification will bestudied via theoretical arguments carried out at a n onrigorous, heuristic level and via simulationexercises on the part of students. Although we will go through theoretical arguments in class insome detail, and stud ents will be expected to understand and be able to carry out similar argu-ments at the same level, our main obj ective will be to appreciate the implications of the results forpractice rather than the technical details. Implementation of the metho ds and application to datawill be emphasized in the homework assignments.Prerequisites: ST 512R, ST 552, familiarity with SAS or R/Splus and a scientific computinglanguage (e.g. MATLAB, FORTRAN, C++, SAS IML, etc). Students should have a strong back-ground in probability and inference at the level of ST 521–522 (the prerequisites for ST 552).Class Web Page: Homework assignments, solutions, and other course material will be availableat http://www.stat.ncsu.edu/people/davidian/courses/st762/. Important announcementsmade in class will also be posted here.Grading: Grades will be based on completion of the following:• Homework: There will be six homework assignments at roughly two-to-three week intervals.Homeworks will contain both analytical problems and data analysis problems and will behanded out in two parts: Problems to turn in (generally 1 or 2) and extra problems n ot to beturned in. Students may work with one another, but each student must independently writethe programs for the data analysis problems and the final solutions to analytic problems to beturned in. Although only 1 or 2 problems are to be turned in and graded for each assignment,you are responsible for the material covered in all problems (graded and extra).Tentative homework due dates: 9/8, 9/22, 10/13, 11/3, 11/17, 12/1Homework will be collected at the beginning of class on the date it is due. It should beneat, all work should be shown, and no late homework accepted unless prearranged with theinstructor. There will be no exceptions to this policy. For problems where programming isrequired, both the program and its output should be turn ed in.• Take-home data analysis project: Midway through the course, you will be provided with adescription of a challenge facing an investigator and the scientific questions s/he wishes toaddress. You will carry out a complete analysis and w rite a formal report (typed) for theinvestigator. This will be a “closed” assignment; that is, you must work independently, notconsulting with one another or, for that matter, with anyone (even your mother). Studentsmay of course use the class notes and ask questions of the instructor.Tentative dates: Handed out 10/13, due 10/20• In-class, closed book test: A two-hour evening period w ill be scheduled during which you willcomplete some an alytical and short-answer exercises. Anything covered in the course up tothe point of the test will be fair game, and ungraded h omework problems from homeworksassigned so far could form the basis for midterm problems.Tentative date: Evening of 11/5• Final Project: In early November, students will be placed in groups, and each group willbe assigned at r an dom to read a recent paper or related s et of papers from the literatur einvolving extensions of material covered in class. There will be two parts to this assignment:1. Brief summary paper: Each student will prepare independently of his/her groupmatesa brief (no more than 5 double-spaced pages) written summary of the paper(s). Thesummary should provide, in the student’s own words, a high-level (n o technical details)description of what the paper(s) is(are) abou t and why the work is important, and abrief discussion of how the work is related to/extend s topics covered in class. This papershould be something a person with ad vanced training in statistics and the material inthis course but not necessarily familiar with the topic could go to to get a general idea ofwhat the paper(s) is(are) about. T he student’s paper should use the notation developedin class.Due date: This will be due on the day of the presentations (see next item)2. Group presentation: Each group will give to the rest of the class a joint oral presentationsummarizing the papers. The size of the groups will be determined by the size of theclass.Due date: The presentations will take place during the scheduled final exam period. Wewill try to choose an earlier time if possible.More details on the project will be provided later in the course.The course grade will be determined according to the following breakdown: homework, 10%; dataanalysis project, 30%; in-class test, 35%; sum mary paper, 10%; oral presentation, 10%; and instruc-tor’s discretion, 5%. The instructor’s discretion portion w ill be based on attendance, participationin class, and instructor’s assessment of mastery of the material.Conversion of these scores into letter grades will be made according to th e following scheme (exceptfor 100, the upper s core in each range belongs to the next highest grade): A, 92–100; A−, 90–92;B+, 88–90; B, 82–88; B−, 78–82. C, 70–78. Scores below 70 will be handled on a