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

P-value calculator page

• Week 1

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

    • Chi Squared Data

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

    • Chi Squared SPSS Output

    • Greek Letters

    • Hesson-McInnis's Matrix Algebra Notes

    • Wilikinson and APA's Statistical Task Force (1999) Article

    • 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)

    • Matrix Inversion Notes

    • Inversion and Regression Syntax

    • Inversion and Regression Output

    • Data

    • HW #1

    • Syntax to run HW #1

    • Answer Key for HW #1

• Week 2

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

    • Lecture

    • Data Used in Lecture

    • Syntax Used in Lecture

    • Output from Lecture

      • R Syntax

      • SAS Syntax

      • Mplus Syntax

      • Mplus Data

    • Holmbeck, 2002

    • Link to Preacher Moderation Materials

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

    • Lecture -- Conceptual Portion

    • Lecture -- SPSS Portion

    • Data for Example in Lecture

    • Syntax for mediation example in class

    • Baron & Kenny, 1986

    • Syntax for bootsrapped regression in SPSS using nonlinear regression

    • Moderated Mediation Syntax from Class

    • Output from class

    • Link to Preacher and Hayes Mediation Script and Material

    • Link to Preacher and Hayes Moderated Mediation Material

    • Shrout and Bolger (2002) on why we should bootstrap mediation

    • Fritz & and MacKinnon (2007) on required sample size to detect mediation

    • HW #2

    • Data for HW #2

    • Syntax to run HW#2

    • Answer Key for HW#2

• Week 3

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

    • Lecture

    • Vitamin C Data for Class Example

    • Syntax from Class

    • Output from Class

    • Cohen, 1968

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

    • Titanic Data for Class

    • Chapter on Titanic Data

    • Syntax from Class

    • Output from Class

    • Wald (1943) on Wald Testing

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

    • Schafer and Graham (2002) on Missing Data

    • Data for HW #3

    • HW #3

    • Syntax to run HW#3

    • Answer Key for HW#3

• Week 4

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

    • Lecture

    • Gill, 2001

    • Data from Class

    • Syntax from Class

    • Output from Class

    • Walk through of output with additional notes on GzLM

    • Nelder & Wedderburn (1972)

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

    • Lecture

    • Hotelling (1931)

    • Wilks (1932)

    • Pillai (1955)

    • Roy (1939)

    • Data from Class (MANOVA from Matrix in SPSS File)

    • Syntax from Class

    • Output from Class

    • Data for HW #4

    • HW #4

    • Syntax to run HW#4

    • Answer Key for HW#4

• Week 5

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

    • Hotelling's T squared

    • Wilks' Λ for one way MANOVA (4 groups)

    • Syntax from Class

    • Nutrition Intervention Data

    • MANCOVA Data (Masculinity, Femininity, SES)

    • Output

  • 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

    • Mauchley (1940)

    • Greenhous & Geisser (1959)

    • Huynh & Feldt (1976)

    • Steve's thesis data for multiple outcomes on repeated measures

    • Long Version of the Riseby Data for Multilevel Model

    • Syntax for all analyses

    • Output

    • Midterm Exam - Take Home Portion

    • Midterm Exam Data for Take Home Portion

    • 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!

    • MANOVA Data from Class Example

    • MANOVA Syntax from Class Example

    • MANOVA Output from Class Example

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

    • Midterm Examination

    • Answer Key to Midterm Examination - In Class Section

    • Data for HW #5

    • HW #5

    • Syntax to run HW#5

    • Answer Key for HW#5

• Week 7

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

    • Readings

      • Hedeker (2004)

      • Kahn (2011)

      • Kahn & Schneider (2013)

      • Pike et al. (2012)

      • SPSS Technical Report on Linear Mixed Effects Models

      • Singer (1998) on SAS for MIXED

      • Peugh and Enders (2005) on SPSS for MIXED

      • Peugh and Enders using GUI

      • SPSS Help on Generalized Linear Mixed Models

    • Riesby study for normally distributed outcome data

      • Data file for Riesby study

      • linear mixed model syntax

      • linear mixed model with no random effect, random intercept, random trend, quadratic, and level 2 predictorl

    • Riesby study with binomial data

      • Data file for Riesby study

      • generalized linear mixed model syntax for binomial datal

      • generalized linear mixed model for binomial data treating time as ordinal (notice the pretty graph)

      • generalized linear mixed model for binomial data treating time as continuous

    • Anticonvulsant study with Poisson data

      • Data file for anticonvulsant study

      • generalized linear mixed model syntax for Poisson data

      • generalized linear mixed model output for Poisson data

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

    • Hotelling (1933)

    • Notes on Eigenvalues and Eigenvectors

    • Keith Widaman presentation on PCA

    • Data for class example PCA

    • Syntax for class example PCA

    • Output for class example PCA

    • Notes to correspond to class example

    • Data for HW#6

    • HW#6

      • Watson, Clark, & Tellegen (1988)

      • PANAS-X Manual

    • Syntax to run HW#6

    • Answer Key for HW#6

• Week 8

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

    • Factor Analysis Notes

    • Spearman (1904)

    • Restructured PANAS Data Set

    • Kahn (2006) on factor analysis

    • Parallel Analysis Program

    • O'Conner's (2000) article about the Parallel Analysis Program

    • Syntax to run parallel analysis program on PANAS data

    • SPSS Syntax for PANAS EFA

    • SPSS Output from PANAS EFA

    • Browne's Comprehensive Exploratory Factor Analysis (CEFA) Program

    • CEFA Manual

    • Input file for PANAS data for CEFA

    • Command file for PANAS for CEFA (varimax rotation)

    • Output file for PANAS from CEFA

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

    • Cattell page on modes of factor analysis

    • Handout on extraction and rotation

    • Browne (2001) on rotation methods

    • Curran, West, and Finch (1999) on Non-Normal Data

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

    • Swain (1975) on factor extractions

    • Crawford and Ferguson (1970) on factor rotations

    • Lee (2010) reviewing the CEFA program

    • SPSS PANAS Data

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

    • SPSS Output for rotated factor solutions

    • CEFA Input File

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

    • CEFA Output File for CF Orthogonal Varimax Rotation

    • CEFA Command File for Targeted Factor Analysis

    • CEFA Output File for Targeted Factor Analysis

    • CEFA Command File for Oblique CF Quartimax

    • CEFA Ouput File for Oblique CF Quartimax Rotation

    • CEFA Command File for Yates's Geomin Rotation

    • CEFA Output File for Yates's Geomin Rotation

    • Larsen and Diener (1987) article that corresponds to homework

    • HW#7

    • Data for HW 7 in SPSS

    • Data for HW 7 in CEFA

    • Syntax to run HW#7 parallel analysis

    • Syntax to run HW#7 EFA in SPSS

    • CEFA Command File 1 for Homework

    • CEFA Command File 2 for Homework

    • Answer Key for HW#7

• Week 9

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

    • Structural Equation Modeling Notes

    • LISREL Notation Handout

    • Joreskog (1969) on confirmatory factor analysis

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

    • Link to the student version of LISREL

    • PANAS Data as .dat file for input

    • LISREL syntax for input - 2 correlated factors (oblique)

    • 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)

    • LISREL syntax for input - 1 factor

    • LISREL output - 1 factor

    • LISREL diagram - 1 factor

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

    • Bryant & Yarnold (1995)

    • PANAS Data as .dat file for input

    • LISREL Matrices

    • LISREL input for model with "subscales"

    • LISREL output for model with "subscales"

    • LISREL diagram for model with "subscales"

    • LISREL input for "Y/eta" model with parcels

    • LISREL output for "Y/eta" model with parcels

    • LISREL diagram for "Y/eta" model with parcels

    • Center for Epidemiological Studies Depression Inventory (CESD) Documentation

    • CESD Data

    • LISREL CESD syntax for hierarchical model

    • LISREL CESD output for hierarchical model

    • LISREL CESD diagram for hierarchical model

    • Handout for in-class exercise

    • LISREL input file with just data for in-class exercise

    • 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)

    • SPSS Data for Multivariate Regression Example

    • SPSS Syntax for Multivariate Regression Example

    • SPSS Output for Multivariate Regression Example

    • Data for LISREL for Multivariate Regression Example

    • LISREL Syntax for Multivariate Regression Example

    • LISREL Output for Multivariate Regression Example

    • LISREL diagram for Multivariate Regression Example

    • Wright (1920)

    • Modified LISREL Syntax to turn Multivariate Regression Example into full Path Model

    • LISREL output for Path Model

    • LISREL diagram for Path Model

  • 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

    • LISREL Syntax from last class examining indirect effects

    • LISREL Output from last class examining indirect effects

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

    • Mueller LISREL syntax for men

    • Mueller LISREL output for men

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

    • Mueller LISREL syntax for women

    • Mueller LISREL output for women

    • Mueller LISREL output for men constraining two paths to be equal

    • Mueller LISREL syntax for pooling men and women

    • Mueller LISREL output for pooling men and women

    • Mueller LISREL syntax for equating Phis

    • Mueller LISREL output for equating Phis

    • 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)

    • Mueller LISREL syntax for men constraining two paths to be equal

    • Mueller LISREL syntax equating Phis and Gammas

    • Mueller LISREL output equating Phis and Gammas

    • Mueller LISREL syntax equating Phis, Gammas, and Betas

    • Muelller LISREL output equating Phis, Gammas, and Betas

    • Mueller LISREL syntax equating Phis, Gammas, and elements of beta

    • Mueller LISREL output equating Phis, Gammas, and elements of beta

    • Corrected Mueller File (notice differences in correlations and SDs)

    • Joreskog (1970)

    • Bentler & Weeks (1979)

    • McArdel & McDonald (1984)

    • Link to the full version of LISREL trial (15-day trial)

    • Happiness Latent Variable Path Model Document

    • LISREL Syntax for Happiness Latent Variable Path Model

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

    • Breckler (1990)

    • Reporting Structural Equation Modeling

      • Raykov, Tomer, & Nesselroade (1998)

      • Boomsma (2000)

      • McDonald & Ringo Ho (2002)

      • Boomsma, Hoyle, & Panter (2012)

      • Hoyle & Isherwood (2013)

    • 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!)

    • Hotelling (1935)

    • Canonical Correlation Macro in SPSS

    • Our favorite PANAS Data

    • 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)

    • UCLA Annotated Canonical Correlation Page

    • North Carolina State University Canonical Correlation Page

    • Sherry & Henson (2005)

    • Thompson (1995)

  • Day 2 - Final Exam

    • Final Exam

    • Answer Key for Final Exam - In Class Section

Some Journals

• The American Statistician

• Behavior Research Methods, Instruments, & Computers

• British Journal of Mathematical and Statistical Psychology

• Educational and Psychological Measurement

• European Journal of Research Methods for the Behavioral and Social Sciences

• Journal of the American Statistical Association

• Journal of Educational and Behavioral Statistics

• Journal of Mathematical Psychology

• Journal of Statistical Software

• Measurement

• Multivariate Behavioral Research

• Organizational Research Methods

• Psychological Assessment

• Psychological Methods

• Psychometrika

• Sociological Methodology

• Statistical Methodology

• Structural Equation Modeling

• Theory & Psychology

• Understanding Statistics

Some Sites

• Advanced Training Institute on methodology sponsored by the American Psychological Association

• American Educational Research Association

• American Statistical Association

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

• G*Power

• Kris Preacher's utilities at quantpsy.org

• Mediation and Moderation

  • Hayes

  • Kenny

  • MacKinnon

  • Preacher

• 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

• Psychometric Society

• Society for Multivariate Experimental Psychology

• Statistics in Mental Health Research Group of the American Statistical Association

• Stats Camp

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