Ed Psych 584

Applied Multivariate Statistics in Educational and Psychological Research
EdPsych/Soc 584 and Psych 594
C.J. Anderson
Spring 2017

Last revised: May 1, 2017

General Information

Announcements

Lecture Notes

Homework and Exams

Handy program and links

Questions or problems regarding this site should be sent to cja@illinois.edu.

General Information :

Syllabus (2017).

Announcements:

May 1:
- I know that there were problems with connecting to the remote desktop server over the weekend. The problem was found and will be corrected within 15 minutes (current time is May 1, 2017, 9:34am)
- Homework 10 answer key is posted below.
- Factor Analysis Lab tomorrow. Bring your laptop. The instructions and data are posted after factor analysis notes
- I will answer questions about exam tomorrow in class (if there are any).
- ICES forms will be distributed tomorrow. I value your comments and suggestions (I have some changes and improvements already in mind for next time).
April 18:
- Answer keys for homeworks 7 & 8 posted along with SAS.
- Lecture notes on Mokken up-dated
- Homework 10 was posted (the last one)
- Final exam and data posted
April 10:
- Notes and data for graphing lecture posted.
- Up-dated notes on Canconical correlation posted
- Homework 9 posted
- Homework 11 posted
- Due date for final will be May 8th. NOT LATE FINALS.
April 7: Materials for SAS graphics lab on Tuesday are posted below.
March 29: Homework 7 is due April 6 and homework 8 is due April 13.
March 28: You may do corrections to you mid-term. Instructions for this are
here. They are due at the beggining of Lecture, Thursday March 30th. No late corrections will be accepted because we will go over the answers in lecture on Thursday
March 14: Homework 7 is posted and due April 6.
Mar 8:
- Mid-term Exam is posted.
- All answer keys and computer code for homeworks are posted
Mar 6: NO LATE HOMEWORK FOR #6---DUE IN CLASS. Mid-term will be posted Thursday March 9th.
Feb 21: We will work on computer part of Homework 6th in lecture either on Tue Feb 28th or Thursday March 2nd. The write up will be due March 9. No late assignments.
Feb 6: Homework 3 is posted and is due Thursday Feb 16
Feb 1: Due date for homework 2 is Tuesday (in lecture) Feb 7.
Jan 30: Answers and SAS (and R thanks to Wes) for homework 1 are posted.
Jan 24
- I posted the data set for the first problem on the first homework.
- Homework #2 is posted in case you want to work ahead.
Jan 17
- First homework: login in to remote2.webstore.illinois.edu BEFORE next class! If you have trouble send me email.
- Introduction sessions to SAS will be given on Tuesday, January 24, 9-10am, rm 22 Education Building. Bring a laptop to the session and be sure that you can login to remote2.webstore.illinois.edu before the sesson.
- A bit of help on homework 1--- you need to compute the angle between two vectors, say x and y, assuming that you have computed the length of x and y (i.e., Lx and Ly), the SAS code (with comments) for this would be
  cos_x_y = x`*y/(Lx*Ly);
  
  * compute inverse of cos and answer given in terms of radians;
  rad_x_y = arcos(cos_x_y);
  
  * create a scalar equal to pi;
  pi = constant('Pi');
  
  * convert radians to degrees;
  degree_x_y = (180/pi)*rad_x_y;

Computing: We will be running the SAS statistical software (SAS) using remote desktop to a university server. Here are the instructions: Instructions. MAC users will have to download a (free) version of the remote desktop application. Note that when you are asked for computer by the remote desktop program, "remote2.webstore.illinois.edu".

There are a few things that you need before you can connect to the remote server:
- Your computer must be hooked up to the internet. If you access the internet via campus wireless, home, hotel, Espresso Royal, or elsewhere).
- You must have the remote desktop application. Those running windows already have it, but those using a MAC, then you will need to download remote desktop server software.
- You must run the VPN software to get behind the UofI firewall. See VPN (Virtual Private Networking)
- You must be registered for the class. If you reccently registered, you may not yet have permission to login.

Lecture Notes:
Suggestion: Only print/download one or two lectures at a time. I sometimes make changes to the notes.
- Introduction
  - Homework Log into you account on remote2.webstore.illinois.edu by the following lecture.
  - Knowing the world graphic. (dated but makes a point.
  - SAS example: some graphics.
  - Using SAS assist for graphics.
- Linear Algebra.
  - Chapter by Larry Hubert..
  - Link to online matrix reference mannual by Mike Brookes.
  - Link to Online Matrix Cookbook..
  - MATLAB presentation by Larry Hubert..
  - SAS information and example:
    - SAS PROC/IML example. IML is short for "interactive matrix language". and what's new. This is also available online when you're running SAS.
    - This document that has all SAS IML commands that I think you will need this semester.
    - SAS IML online documentation
    - SAS IML documentation in pdf. You can print sections or chapters and it is easy to search (i.e., see Chapter 23 Language Reference which starts on Page 543).
  - R example
    - R script from lecture notes.
    - scores_data.txt. The data used in R.
    - basic_statistics_R.txt. Reading in data and computes sample statistics. This also shows how to write functions and use them.
    - An R function that implements "Useful Matrix Formula". Reading in data and computes all sample statistics in a single function (with comments. This also shows how to write functions and use them.
- Optional: Introduction to SAS to be held Tuesday, January 24, 9-10am, rm 22 Education Building. Bring a laptop to the session and be sure that you can login to remote2.webstore.illinois.edu before the sesson. We will go over at least the first and the second time permiting:
  - hsb-data.sas.
  - SAS PROC/IML example. IML is short for "interactive matrix language". We went over part of this in lectre.
  - Using SAS assist for graphics.
- Geometry of the Sample.
- Linear Combinations.
- Multivariate Normal Distribution.
- Inferences About a Mean Vector
  - SAS/IML: WAIS example.
  - SAS/IML: 4 Psychological tests example. (including how to read data into SAS/IML, and showing the relationship between T^2 and Wilk's lambda).
- Comparisons of Two Means.
- More Linear Algebra: eigensystems, SVD & maximization.
  - Overview/Summary Handout.
  - SAS/IML: Two independent sample T test.
  - SAS: IML and Biplot.
  - Biplots in Practice by Michael Greenacre... for more information about bi-plots.
  - Least Squares Optimization in Multivariate Analysis by Jos M.F. ten Berge...for more information on linear algebra and applications to multiple regression, principal compenents analysis, simultaneous components analysis in two or more populations, MINRES factor analysis, canonical correlation, redunancy analysis, PARAFAC and INDSCAL.
  - For additional resources, see linear algebra notes above.
- Principal Components Analysis.
  - Biplots in Practice by Michael Greenacre
  - Least Squares Optimization in Multivariate Analysis by Jos M.F. ten Berge...for more information on linear algebra and applications to multiple regression, principal compenents analysis, simultaneous components analysis in two or more populations, MINRES factor analysis, canonical correlation, redunancy analysis, PARAFAC and INDSCAL.
  - SAS: European Jobs.
  - SAS: Swiss Bank Notes
  - Picture of Swiss Bank Note (variables labeled aren't quite what we're using).
  - SAS: Men's Track Data
  - SAS: Scree Plots for all examples.
  - SAS iml module implementing Bartlett's test that last r eigenvalues are equal. This should be used only on sample principal components (or other use of eigendecomposition).
- One-Way MANOVA.
  - SAS: Shorthand example.. This uses PROC GLM and in PROC/IML rank g design matrix.
  - SAS: Cameron-Pauling cancer data example. This uses PROC GLM, and in IML, rank (g+1) design matrix, traditional method. Computing various contrasts are illustrated here.
- Extensions of one-way MANOVA.
  - SAS: WAIS and Eldery. (profile analysis example).
  - SAS: shorthand example revisited. (2-way MANOVA).
  - SAS: unbalanced design example.
- Discriminant Analysis
  - Lecture Notes.
  - SAS:WAIS example. (2 group analysis).
  - SAS:Shorthand example: (6 groups) SAS PROCS GLM, IML, CANDISC, and DISCRIM.
- SAS Graphics for Multivariate Analysis. This document contains SAS code for some useful graphs in multivariate analysis. The data used and a short paper are below.
  - Psych test scores. These data are used in notes for
    - uni and bivariate distribution in a lattice plot
    - scatter plot of first 2 principal compenents with different color for boys & girls
    - scree plot (PCA)
    - variance explained (PCA)
  - Eurpean jobs data for Scatter plot of first 2 principal compenents with text identifying observations.
  - GMAT data for plots of discrimant functions
  - Dementia Data for plots that you might use in profile analysis.
  - Tips and Tricks: Using SAS/GRAPH Effectively Massengill, A.D. (Paper 90-30). SAS Insitute, Cary, NC.
- Canonical Correlation Analysis
  - Lecture Notes.
  - Link to Heck (1960). (Will only work if have uiuc account or jstor).
  - Link to Pillai & Bantegui (1959). (Will only work if have uiuc account or jstor).
  - SAS IML code to compute approximate percentiles of greatest root distribtion. This is based on paper by Iain Johstone (2002, in Ann.Appl. Stat, 3(4), 1616-1633).
  - SAS: WAIS example. (how to input a correlation matrix as a data set, PROC CANCOR).
- Mokken Scale Analysis
  - Lecture Notes: brief introduction to Mokken scale analysis.
  - Data for R.
  - R for mokken example.
  - van der Ark (2012). New Developments in Mokken Scale Analysis in R. Journal of Statistical Software.
- Factor Analysis
  - Lecture Notes. or an alternative format (but otherwise equivalent version)
  - SAS MACRO that does item analysis. This macro runs PROC CORR and uses PROC IML to test hypotheses on Cronbach's alpha and provides (1-alpha)x100% confidence intervals for alpha.
  - SAS Macro that does Item Analysis, Cronbach alpha CI & tests, Factor Analysis. (this macro uses PROCs CORR, IML and Factor).
  - SAS for example presented in class & more. (Espelage Bully data).
  - SAS for 2nd example presented in clas. (Holtzinger & SwineFord 1939: 5 test scores).
- Factor Analysis: LAB
  - Lab instructions May 2, bring laptop.
  - Data to be used.
  Homework & Exams:
  - Homework writing guidelines..
  - Link to R homepage.