# Multivariate Statistics

**Multivariate Statistics (HPSC511 – Psychological Statistics 2)**

**Multivariate Statistics (HPSC511 – Psychological Statistics 2)**

Dates Correspond to the Spring, 2011 Syllabus, but the topics and links are up to date.

The overarching goal is to develop knowledge of multivariate statistical techniques, their appropriate application to data derived from different designs, their limitations, and how to interpret results. Additionally, I hope you will see connections between various techniques used in this class. In addition to covering the chi-squared test from univariate statistics, the course focuses on matrix formulations of regression and applications thereof (i.e., dummy coding of categorical variables for regression, moderation, and mediation), multivariate analysis of variance (MANOVA), generalized linear models (including logistic and Poisson regressions), linear mixed modeling, generalized linear mixed modeling, generalized estimating equations, principle components analysis, exploratory factor analysis, and structural equation modeling (i.e., confirmatory factor analysis, path analysis, and covariance structure modeling), and canonical correlation. When possible, SPSS will be used.

PRIOR TO 2014: For exploratory factor analysis, comparisons between SPSS and the free Comprehensive Exploratory Factor Analysis (CEFA) software will be made. Structural equation modeling will be conducted using LISREL.

2014 and Beyond: For exploratory factor analysis and structural equation modeling, we will use Mplus. The files associated with it may be found on D2L.

Syllbaus (Winter 2017-2018) - updates will be available through D2L

Syllbaus (Winter 2016-2017) - updates are available through D2L

Syllbaus (Winter 2015-2016) - updates are available through D2L

Syllabus (Spring 2015) - updates are available through D2L

Syllabus (Spring 2014) - updates are available through D2L

Syllabus (Spring 2013)

Syllabus (Winter 2011-2012)

Syllabus (Spring 2011)

Companion Website for Using Multivariate Statistics (5th ed.) - 2011 and 2012 versions of the class

Companion Website for Using Multivariate Statistics (6th ed.) - 2013 Version of the class

Week 1

Day 1, Monday, February 28, 9:00 - 11:00 (Matrix Algebra and Chi-Squared [left over from Stats 1])

Chi Squared SPSS Syntax *this link needs to be revised -- it's different syntax (though not unuseful)

I find this document useful for thinking about clean data: link

A video on examining normality

Day 2, Wednesday, March 2, 6:45 - 8:45 (Matrix Formulations of Multiple Regression)

Week 2

Day 1, Monday, March 7, 9:00 - 11:00 (Moderation and Simple Slopes)

Day 2, Wednesday, March 9, 6:00 - 8:00 (Mediation)

Week 3

Day 1 - Monday, March 14, 9:00 - 11:00 (Dummy Coding, Moderation with Continuous and Categorical, and Quadratic/Polynomial Effects)

Day 2 - Wednesday, March 16, 6:00 - 8:00 (Logistic Regression and Discriminant Function Analysis)

Wald (1943) on Wald Testing

Box (1949) on Equality of Covariance Matrices (and more general things)

Schafer and Graham (2002) on Missing Data

Week 4

Day 1 - Monday, March 21, 9:00 - 11:00 (Generalized Linear Models [GzLM])

Day 2 - Wednesday, March 23, 6:00 - 8:00 (Multivariate Analysis of Variance [MANOVA])

Lecture

Data from Class (MANOVA from Matrix in SPSS File)

Week 5

Day 1 - Monday, March 28, 9:00 - 11:00 (MANOVA and Multivariate Analysis of Covariance [MANCOVA])

Day 2 - Wednesday, March 30, 6:00 - 8:00 (Repeated Measures MANOVA and Intro to Multilevel Modeling [Midterm Examination Take Home Portion Set])

Lecture

Wide Version of the Riesby Data for Repeated Measures ANOVA and MANOVA

Steve's thesis data for multiple outcomes on repeated measures

Syntax to run Midterm Exam

Answer Key for Midterm Exam - Take Home Section

Week 6

Day 1 - Monday, April 4, 9:00 - 11:00 (Catch Up and Review Day)

no lecture other than catching up -- please bring your questions!

Midterm Examination In Class - April 6, 6:00 - 8:00

Midterm Examination

Answer Key to Midterm Examination - In Class Section

Week 7

Day 1 - Monday, April 11, 9:00 - 11:00 (Linear and Nonlinear Mixed Modeling)

Readings

Riesby study for normally distributed outcome data

Riesby study with binomial data

Anticonvulsant study with Poisson data

Day 2 - Wednesday, April 13, 6:00 - 8:00 (Principal Components Analysis)

Notes to correspond to class example

Week 8

Day 1 - Monday, April 18, 9:00 - 11:00 (Exploratory Factor Analysis; EFA)

Day 2 - Wednesday, April 20, 6:00 - 8:00 (EFA and Factor Rotation)

Browne (2001) on rotation methods

Fabrigar, Wegener, MacCallum, & Strahan (1999) on exploratory factor analysis

SPSS Syntax for varimax and directly oblimin with kappa = 0 (i.e., quartimax) rotation

CEFA Command File for Crawford-Ferguson (CF) Varimax Rotation

Larsen and Diener (1987) article that corresponds to homework

Week 9

Day 1 - Monday, April 25, 9:00 - 11:00 (Confirmatory Factor Analysis; CFA)

Joreskog (1969) on confirmatory factor analysis

Hu & Bentler (1999) on cutoff criteria for fit statistics

LISREL output - 2 correlated factors (oblique)

LISREL diagram - 2 correlated factors (oblique)

LISREL syntax for input - 2 uncorrelated factors (orthogonal)

LISREL output - 2 uncorrelated factors (orthogonal)

LISREL diagram - 2 uncorrelated factors (orthogonal)

Day 2 - Wednesday, April 27, 6:00 - 8:00 (CFA)

Center for Epidemiological Studies Depression Inventory (CESD) Documentation

HW#8

Syntax to run HW#8

Answer Key for HW#8

Week 10

Day 1 - Monday, May 2, 9:00 - 11:00 (Multivariate Regression and Path Analysis)

Day 2 - Wednesday, May 4, 6:00 - 8:00 (Path Analysis, Indirect Effects, and Multi-Group Path Analysis)

Data for LISREL for Multivariate Regression Example from Last Class

Mueller (1998) Article to correspond to Path Analysis Example #2

Mueller LISREL diagram (note: I only include one, as they all look the same)

Mueller LISREL output for men constraining two paths to be equal

HW #9

Syntax to run HW#9

Answer Key for HW#9

Week 11

Day 1 - Monday, May 9, 9:00 - 11:00 (Multi-Group Path Analysis and Covariance Structure Modeling)

Day 2 (Covariance Structure Modeling; Final Examination Take Home Portion Sent, Key for HW #9 Sent)

Reporting Structural Equation Modeling

Final Exam

Data for Final Exam

Syntax to run Final Exam

Answer Key for Final Exam - Take Home Section

Week 12

Day 1

Catch Up and Review Day / Summary of Multivariate Statistics (no lecture planned other than catching up -- please bring your questions!)

Canonical Correlation Syntax to call macro and to run MANOVA canonical correlation

Canonical Correlation Output as PDF (looks messy)

Canonical Correlation Ouput in SPSS (looks nice, but requires SPSS to open)

Day 2 - Final Exam

Final Exam

Answer Key for Final Exam - In Class Section

Some Journals

Some Sites

Advanced Training Institute on methodology sponsored by the American Psychological Association

Division 5 of the American Psychological Association (Measurement, Evaluation, & Statistics)

Kris Preacher's utilities at quantpsy.org

Mediation and Moderation

Meehl's APS address from 1998 reprinted in A Paul Meehl Reader, "The Power of Quantitative Thinking" (link)

The Methodology Center at Penn State University

Statistics in Mental Health Research Group of the American Statistical Association

University of Michigan Inter-university Consortium for Political and Social Research Summer Program in Quantitative Methods of Social Research