STA 431S 2011

Structural Equation Models

University of Toronto Mississauga, Winter/Spring 2011

Lecture: Tuesday 11:10-1:00 in Kaneff Room 132 and Thursday 11:10-12:00 in the South/Davis building, Room 1130.

Tutorial: Friday 11:10-12:00 in the South/Davis building, Room 2068

(A quiz will be given in each tutorial.)

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

A mistake in Assignment 10 Question 6 has been fixed. Notice that what we're doing is building up the 3-variable rule for standardized varibles.

Just a comment on the SAS part of the final assignment: There are no coefficients on the straight arrows in the path diagram, but that does not mean the factor loadings necessarily equal one. Would it make sense?

A nasty error on the final assignment has been fixed (April 7th). I was typesetting the assignment in LaTeX, and some LaTeX code got mixed in with the SAS code in that data step I suggested you copy. The result was poison. After country there's just a dollar sign and a semi-colon. Sorry about that.

More office hours are listed on the Final Exam information page.

• Final Exam Information: Last revised Thursday April 7th.
• Course Outline
• Computing Information and Links, including documents on R, unix/linux, and SAS.
• Homework Assignments
  1. Assignment 1: Quiz in tutorial Friday Jan. 14th
  2. Assignment 2: Quiz in tutorial Friday Jan. 21st
  3. Assignment 3: Quiz in tutorial Friday Jan. 28th
  4. Assignment 4: Quiz in tutorial Friday Feb. 4th
  5. Assignment 5: Quiz in tutorial Friday Feb. 11th
  6. Assignment 6: Quiz in tutorial Friday Feb. 18th
  7. Assignment 7: Quiz in tutorial Friday March 4th
  8. Assignment 8: Quiz in tutorial Friday March 11th
  9. Assignment 9: Quiz in tutorial Friday March 18th
  10. Assignment 10: Quiz in tutorial Friday March 25th
  11. Assignment 11: Quiz in tutorial Friday April 1st
  12. Final Assignment: A few more questions to help you prepare for the final exam, including the SAS part.
• Handouts and Overheads: You may want to print these and bring to class so you can write notes on them.
  1. First part of day 1 lecture: All this and more is in Chapter 0.
  2. Part 2 about regression with measurement error
  3. Part 3 about regression with measurement error. This includes some "review" material on large sample theory. Some of this material will be in the next version of the Appendix, which I will post after Quiz 1. It starts with the results of the big simulation study. The typo that mis-labelled the correlation between X₁ and X₂ as "reliability" has finally been corrected.
  4. SAS Handout 1
  5. Goodness of Fit and model fitting.
  6. Double measurement regression with SAS proc calis: A simple scalar example.
  7. Correlated Measurement Error: A non-identifiable double measurement model.
  8. Conditional and unconditional regression with no measurement error.
  9. Double Measurement Regression: A general matrix treatment. This is an improvement over earlier lecture material.
  10. Analysis of the BMI Health Data
  11. Likelihood Ratio Tests: A short piece
  12. Structural Equation Models: A general introduction (at last)
  13. Factor Analysis Part One: Exploratory Factor Analysis
  14. Exploratory Factor Analysis of the twin data
  15. Exploratory Factor Analysis of some simulated data: Why you should never do exploratory factor analysis
  16. Confirmatory Factor Analysis Part One: Handwritten class notes
  17. Confirmatory Factor Analysis Part Two: Powerpoint slides. The first bit replaces the last 2 pages or so of Part 1.
  18. Identifiability rules.
  19. Applying the rules to path diagrams.
• Textbook: I have taught several versions of this course and have never found a satisfactory textbook. Now I am writing one. The good news is that it's Free, and the bad news is that it's still in the early stages. Here is how we will do it. I will post pieces of the book below, trying to stay ahead of what is covered in lecture. If any of these pieces are revised and re-posted during the course, it will be indicated below. If you are curious, you can go to the Textbook Website. There, you will find links to the current version of the complete book, as well as the LaTeX source code and other supporting materials like graphics files. Be warned! The full version is not ready for public consumption yet, and I cannot recommend it. I hope that by the end of the term it will be worth downloading.
  • Appendix A: Background material. Some of this is pure review, some of it goes beyond the usual preparation but is necessary, and some of it is for advanced topics we may never get to in this course. When in doubt, be guided by the homework problems that are assigned. They represent what you need to be able to do. This is a new version as of Jan. 13th.
  • First 23 pages of Chapter 0: More is to come.
• Data sets from lecture and homework.