**Multivariate forms of multiple linear
regression, analysis of variance and analysis of co-variance. Multiple
discriminant analysis, canonical correlation, and principal-components
analysis. Pre: EDEP 603 and EDEP 604, or
consent. (Cross-listed as PSY 614 and SW 656)**

Modified: August 20, 2006

**Pedhazur, E. J., & Schmelkin, L.
P.** (1991). *Measurement, design, and analysis: An
integrated approach.* Hillsdale, NJ: Elrbaum. [Esp. Chaps. 22, 23,
& 24]

**Pedhazur, E. J.** (1997).
*Multiple regression in behavioral research: Explanation and
prediction* (3rd ed.). Orlando, FL: Harcourt Brace. [Esp. Parts 3
and 4]

**Stevens, J.** (1995). *Applied
multivariate statistics for the social sciences* (3rd ed.).
Hillsdale, NJ: Erlbaum.

**Wickens, T. D.** (1995). *The
geometry of multivariate statistics.* Hillsdale, NJ: Erlbaum.

The student is strongly encouraged to make use of these Internet resouces/links as a way to reinforce one's understanding of basic statistical concepts.

- Electronic Statistical Textbook (from StatSoft)
- Exploratory Factor Analysis (Ledyard Tucker and Robert MacCallum) [downloadable in pdf or postscript format]
- Principal Components Analysis (Caltech)
- Structural Equation Modeling (David A. Kenny, University of Connecticut)

- MacCallum, R. (1998). Commentary
on quantitative methods in I-O research.
*The Industrial-Organizational Psychologist*,**35**(4). (**NB:**Please consider this required reading.) - Minke, A. (1997, January). The Six Two-Mode Factor Analytic Models Paper presented at the meeting of the Southwest Educational Research Association, Austin, TX.
- Preacher, K. J., & MacCallum, R. C. (2003). Reparing Tom
Swift's electric factor analysis machine.
*Understanding Statistics*,**2**(1), 13-43. - Rennie, K. M. (1997, January). Exploratory and confirmatory rotation strategies in exploratory factor analysis Paper presented at the meeting of the Southwest Educational Research Association, Austin, TX.
- Stapleton, C. D. (1997, January). Basic concepts in exploratory factor analysis (EFA) as a tool to evaluate score validity: A right-brained approach. Paper presented at the meeting of the Southwest Educational Research Association, Austin, TX.
- Stapleton, C. D. (1997, January). Basic concepts and procedures of confirmatory factor analysis Paper presented at the meeting of the Southwest Educational Research Association, Austin, TX.
- Yu, C. H., & Behrens, J. T. (1995).
Applications of scientific
multivariate visualization to behavioral sciences.
*Behavior Research Methods, Instruments, and Computers*,**27**, 264-271.

- Data Analysis BriefBook (R. K. Bock & W. Krischer, CERN)
- Factor Analysis Glossary (John T. Pohlmann, Southern Illinois University)

- Ethical Guidelines for Statistical Practice (American Statistical Practice)
- Thompson, B. (2000). A Suggested Revision to the Forthcoming 5th Edition of the APA Publication Manual
- Wilkinson, L. & Task Force on Statistical Inference.
(1999).
Statistical methods in psychology journals: Guidelines and
explanations.
*American Psychologist*,**54**(8), 594-604.

- The SAS Institute
(SAS is available on
**UHUNIX2**to anyone with a UHUNIX account)Running SAS in Batch Mode on Unix (Robert A. Yaffee, NYU)

SAS for UNIX (University of Texas Statistical and Mathematical Services)

- SEM Software Packages (Ed Rigdon, Georgia State University)
- SPSS, Inc.
(SPSS is available on
**UHUNIX2**to anyone with a UHUNIX account) - Student version of AMOS (Free)

PROC CALIS (Structural Equation Model procedure)

- The Comprehensive R Archive Network (CRAN)
- LISREL (Karl Jöreskog & Doug Sörbom) (Free student edition available)
- MacAnova (not just for Macs) (Gary W. Oehlert and Christopher Bingham, University of Minnesota)
- Idanet Software Page (Paul Barrett, University of Auckland)
- Mx (Michael Neale, Virginia Commonwealth University)
- OpenStat (Bill Miller, Iowa State University)
- |Stat (Gary Perlman, UC San Diego)
- StatLib (Carnegie Mellon University)
- The TETRAD Project: Causal Models and Statistical Data (Peter Sprites, Clark Glymour, & Richard Scheines, Carnegie Mellon University)
- ViSta - The Visual Statistics System (Forrest W. Young, University of North Carolina)

- The Data and Story Library (The DASL Project, Cornell University)
- Fathom Resource Center: Data Sets
- Journal of Statistics Education Data Archive
- Statistical Reference Datasets
- StatLib Data Archive

- Education 231A: Multivariate Analysis (Phil Ender, UCLA)
- PA 765: Quantitative Research in Public Administration (G. David Garson, North Carolina State University)
- Psych
431: Latent Variable Models (Phil Wood, University of Missouri)
[
**Highly Recommended**] - Psychology 613: Multivariate Techniques (Bertram F. Malle, University of Oregon)
- Psych 6140: Multivariate Data Analysis (Michael Friendly, York University)
- Psychology 7291: Multivariate Statistics (Gregory Carey, University of Colorado, Boulder)
- Public Administration 765: Quantitative Research in Public Administration (David Garson, North Carolina State University)
- Statistics 407: Methods of Multivariate Anaylysis (Dianne Cook, Iowa State University)
- Statistics 501: Multivariate Statistical Methods (Dianne Cook, Iowa State University)

- SEMNET (Structural Equation Modeling Discussion Network)
- Statistical List Subscription Service (StatTransfer, Circle Systems)
- STUDSTAT@ASU.EDU (A discussion group for students of statistics)

- Eric Weisstein's World of Mathematics: Probability and Statistics (A Wolfram Web Resource)
- InterStat: Statistics on the Internet (A peer-reviewed electronic journal of statistics) [requires Adobe Acrobat Reader]
- SEM FAQ (Ed Rigdon, Georgia State University)
- Measurement FAQ (Warren Sarle, SAS Institute) [If you have not read this, please do so now.]
- NetMul: A WWW online multivariate analysis system (Jean Thioulouse, Université Claude Bernard, Lyon 1)
- Office for Human Research Protections
- Self-Paced Statistical Software Tutorials (University of Texas at Austin Statistical Services)
- StatCalc User Guide: Multivariate
- Structural Equation Modeling: A Special Interest Group of the AERA

We will not be considering the textual material in the order in which it is presented in the book. We will begin with a review of basic psychometric principles (reliability and validity) and the logic of quantitative modeling and statistical inference (parameter estimation and hypothesis testing).

We will first consider the "measurement model" which deals with the dimensionalization of the domain of inquiry or the relation between the latent constructs and the observed indicators we use to assess them. Then we will consider the "structural model" which deals with the interrelations of the dimensions (latent constructs) of the domain.

Since the material with which we will be dealing lends itself most reasonably to representation in matrix algebra notation, there will be class time spent on the basic formulations thereof. Tabachnick and Fidell give an introduction in Appendix A. There is also an introduction to matrix algebra in Appendix A of Pedhazur as well at links to pages on matrix algebra listed in the outline below. The discussion of matrix algebra in class will be centered on the representation of linear models in matrix formulation.

A. Quantitative Modeling in the Behavioral Sciences

1. Measurement and Dimensionalization

2. Theoretical/Structural Modeling

B. Matrix Algebra (representation of models in matrix algebra notation)

Introduction to Matrix Algebra (Bertram F. Malle, University of Oregon)

Matrix Algebra for Statistics (Bertram F. Malle, University of Oregon)

C. Measurement: The Dimensionalization of the Domain of Inquiry

1. Principal Components Analysis (PCA)

2. The Common Factor Model

a. Exploratory Factor Analysis (EFA)

b. Confirmatory Factor Analysis (CFA)

Understanding Factor Analysis (R J Rummel, Emeritus, University of Hawaii)

Programs for Number of Components and Factors using Parallel Analysis (Brian P. O'Conner, Lakehead University, Ontario)

Preacher, K. J., & MacCallum, R. C. (2003). Reparing Tom
Swift's electric factor analysis machine. *Understanding
Statistics*, **2**(1), 13-43.

Eigenvalues: A short introduction (authorship unknown)

Factor Analysis Using SAS PROC FACTOR (Statistical Services, UT-Austin)

Confirmatory factor analysis using SAS (Statistical Services, UT-Austin)

Factor Analysis (G. David Garson, North Carolina State University)

Factor Analysis (Bertram Malle, University of Oregon)

Factor Analytic Models (Leslie F. Marcus, Queens College, CUNY)

Factor Analysis Glossary (John T. Pohlmann, Southern Illinois University)

Review of Exploratory Factor Analysis (Stephen G. Sapp, Iowa State University)

D. Structure: The Canonical Model (estimation of theoretical relation parameters)

1. Estimation based on Ordinary Least Squares (OLS)

a. Analysis of Variance (ANOVA)

b. Analysis of Covariance (ANCOVA)

c. Multiple Regression

Multiple Regression (G. David Garson, North Carolina State University)

d. Discriminant Analysis (dichotomous dependent variable)

Discriminant Function Analysis (G. David Garson, North Carolina State University)

2. Consideration of Multivariate Forms

a. Multivariate Analysis of Variance (MANOVA)

b. Multivariate Analysis of Covariance (MANCOVA)

GLM: MANOVA and MANCOVA (G. David Garson, NCSU)

c. Multivariate Regression

d. Multiple Discriminant Analysis (polychotomous dependent variable)

Discriminant Function Analysis (G. David Garson, NCSU)

Multiple Discriminant Analysis (G. David Garson, North Carolina State University)

3. Estimation based on Maximum Likelihood (MLE)

a. Logistic Regression

Logistic Regression (G. David Garson, North Carolina State University)

b. Structural Equation Modeling

The Form of Structural Equation Models (Ed Rigdon, Georgia State University)

Structural Equation Modeling (G. David Garson, North Carolina State University)

LISREL (University of Texas at Austin)

If you have difficulty with any of the concepts presented in the text or lectures, please consult one or more of the links above or the syllabus for one or more of the courses (with associated links) on my home page. If you are unable to satisfactorily resolve any questions by consulting the appropriate links, please make an appointment with me at your earliest convenience.

Evaluation and assignment of grades

Questions or comments to: daniel@hawaii.edu