STA2201: Methods of Applied Statistics II, Winter/Spring 2006

Structural Equation Models

Lecture: Tuesday 10:10 - 11:00 a.m. and Thursday 10:10 a.m. - 12:00 noon, WI 523.

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

The two factor analysis handouts are available below in case you want an electronic copy. The final handout, on simple measurement error regression with intercept (as well as without) is also available -- but I will bring hard copy for everyone unless the photocopier breaks.

• Course Outline
• Assignments
  1. Assignment 1 (Revised on Dec. 16th): Quiz on Thursday Jan. 19th at the beginning of class.
  2. Assignment 2 (Revised and final version): Quiz on Thursday Jan. 26th at the beginning of class. Data for the computer question are here.
  3. Assignment 3: Quiz on Thursday Feb. 9th at the beginning of class. Data for the computer question are here. Try help(read.table).
  4. Assignment 4: Quiz on Thursday Feb. 16th at the beginning of class. It will be open book and open notes.
  5. Assignment 5: Quiz on Thursday March 2nd at the beginning of class.
  6. Assignment 6: Log and list files are due on Thursday March 16th at the beginning of class.
  7. Assignment 7: The data file mvreg.dat is here. The order of the variables is: X₁, X₂, Y₁, Y₂.

     If you are on fisher, another way to get the data is to type (at the unix prompt)

     cp /dos/brunner/public_html/2201s06/data/mvreg.dat .

     The period is important; it refers to your current directory.

     Log and list files are due on Thursday March 30th at the beginning of class.

  8. Assignment 8: Log and list files are due on Thursday April 6th at the beginning of class.
• In-Class Overheads (Please print and bring to class)
  • Type I error inflation in Multiple regression: You don't actualy have to print this one. It will be presented on the first day of class, and I will bring hard copy for everyone because I do not expect you to find this website before the course begins.
  • A first look at R.
  • Maximum likelihood (and tests) with R.
  • Maximum likelihood on the mutivariate normal with R.
  • The LISREL model notation.
  • Fitting the Little Path Model with R
    • In PDF Format.
    • In Word Format.
    I already distributed hard copy of this. If you copy-paste any of the code, do it from the Word document. PDF files contain invisible characters that can cause trouble.
  • SAS Handout One (SENIC Data): Read and label data, do basic descriptive statistics and a few elementary tests. Hard copy of the first four pages has already been distributed in class.
  • SAS Handout Two (SENIC Data): Descriptive Statistics and a Few Elementary Tests
  • SAS Handout Three (SENIC Data): Ordinary multiple regresssion with proc reg. This used to be called Handout 2.
  • Fitting the Little Path Model (Path0) with SAS
    • In PDF Format.
    • In Word Format.
    If you copy-paste any of the code, do it from the Word document. PDF files contain invisible characters that can cause trouble.
  • Another small path model (Path1), observed variables only.
    • In PDF Format.
    • In Word Format.
  • Path1 again, this time reading a sample covariance matrix instead of raw data. Program only (output is exactly the same as for the run with raw data.
    • In PDF Format.
    • In Word Format.
  • Test whether the covariance matrix is diagonal, given a multivariate normal assumption. No model specifications (lineqs) at all.
    • In PDF Format.
    • In Word Format.
  • Test for equality of variances on repeated measures data -- that is, test for equality of diagonal elements of a covariance matrix. No model specifications (lineqs) at all, just same name to specify equal parameter values (could have used lincon). Save outest SAS data set and do Wald test with proc iml.
    • In PDF Format.
    • In Word Format.
  • Surface path model 2 for the SENIC data: This one includes dummy variables for region and medical school affiliation. Its validity depends on robustness of the normal likelihood methods. Fit reduced models with lincon (linear constraints). Calculate likelihood ratio tests with proc iml. Suppress warnings about singularity with the singular= option. The last of four proc calis runs suppresses the output with the noprint option, and writes out a SAS data set with the MLEs and asymptotic covariance matrix with the outest option. Extract the desired information by creating new data sets and using set, if and keep. Extract only the relevant part of the covariance matrix and MLE. Read the data sets into proc imland compute the Wald test and p-value.
    • In PDF Format.
    • In Word Format.
  • Factor Analysis Part I: Single-factor model for simulated data. It's harmlessly non-identified. The likelihood function has two maxima, equal in elevation.
    • In PDF Format.
    • In Word Format.
  • Factor Analysis Part II: Exploratory and Attempted Conformatory Factor Analysis for a Non-identified Two-factor Model
    • In PDF Format.
    • In Word Format.
  • Measurement Error Regression: Simple regression with measurement error, with and without intercepts
    • In PDF Format.
    • In Word Format.

   

• Computing Links and Hints