STA 431F 2009

Structural Equation Models

University of Toronto Mississauga, Winter-Spring 2009

Lecture: Monday 1:10-2:00 in NE257, Wednesday 1:10-3:00 in SE 3093.

Tutorial: Friday 1:10-2:00 in NE 228

This page is under construction, and will be updated frequently throughout the course.

Here is some Information About the Final Exam. Christine's office hours on Friday have changed.

A REVISED Summary of Identification Rules is posted. It is also available under Readings below.

• Course Outline
• Homework Assignments
  1. Assignment 1 (Review): For Quiz 1 on Friday Jan. 16th
  2. Assignment 2 For Quiz 2 on Friday Jan. 23d
  3. Assignment 3 For Quiz 3 on Friday Jan. 30th. Here is a link to the SAT data for Question 2. Please excuse all the rules and threats in Question 2, but this is the first computer assignment, and it is helpful to be very clear about these things right from the start.
  4. Assignment 4 For Quiz 4 on Friday Feb. 6th.
  5. Assignment 5 For Quiz 5 on Friday Feb. 13th.
  6. Assignment 6 For Quiz 6 on Friday Feb. 27th. Here is a link to the wishbone data of Question 6.
  7. Assignment 7 For Quiz 7 on Friday March 6th. Here is a link to org1.data of Question 5.
  8. Assignment 8 For Quiz 8 on Friday March 13th.
  9. Assignment 9 For Quiz 9 on Friday March 20th. Here is a link to littlemath.data of Question 4.
  10. Assignment 10 For Quiz 10 on Friday March 27th. Here is a link to pigs.data of Question 4.
  11. Assignment 11 For Quiz 11 on Friday April 3d. Here is a link to peru.data of Question 5.
• Computer Handouts (Please print and bring to class)
  1. SAS Handout 1: Read and Describe data, Basic multiple regression
  2. SAS Handout 2: A little path analysis with proc calis
  3. SAS Handout 3: sencipath1.sas.
  4. SAS Handout 4: Exploratory Factor Analysis on real data.
  5. SAS Handout 5: Exploratory Factor Analysis on simulated data.
  6. SAS Handout 6: Confirmatory Factor Analysis on the Twin data (first try).
  7. SAS Handout 7: More exploratory work using "confirmatory" factor analysis on the Twin data. This is the revised and corrected handout.
  8. SAS Handout 8: Ordinary regression on the Body Mass Index (BMI) data.
  9. Handout 8.5: An R session illustrating inflation of Type I error rate when measurement error is ignored.
  10. SAS Handout 9: Double Measurement regression on the BMI data.
  11. SAS Handout 10: Full structural equation model for the Language Development data.
  12. SAS Handout 11: Test one more parameter for the Language Development data.
• Readings (To compensate for the lack of a textbook)
  1. Random Matrices
  2. Multivariate Normal Handout
  3. Introduction to unix and SAS
  4. Large-sample Likelihood Ratio Tests (Draft)
  5. Slides Set One: Projected in class Jan. 21st, plus a few more.
  6. Slides Set Two
  7. Summary of Identification Rules
• Background Reading (Optional)
  1. An old book Excellent ideas and path diagrams, all scalar (non-matrix) calculations, and no estimation or inference. Notation is different from ours, but easy enough to follow. This book is written for very motivated graduate students in Sociology, which means that Statistics undergraduates can understand it completely.
  2. Jöreskog (1978) A good introduction for Psychologists from the journal Psychometrika.
  3. Brunner and Austin (2009): Inflation of Type I error rate when measurement error in the independent variables is ignored.
  4. Biostatistics Seminar: Introduction to Structural Equation Models
     • Overheads from Part One: Path diagrams, notation and basic ideas.
     • Overheads from Part Two: SAS proc calis
• Sample programs (and data sets) from lectures and homework.
• Computing Resources for this class (including unix and emacs handouts)
• Tutorial Material: Gifts from Christine

Please note that written solutions will not be provided for the homework problems. The goal is for you to learn by actively working to solve the problems, not just by imitating correct answers. If you do not know how to approach a problem, the first thing to do is look at your class notes. Probably you will find something similar there. If this does not help, please come to office hours and ask! Of course if the difficulty is with review Assignment One, you should start by checking notes and textbooks from the courses where you learned the material.