## Pedhazur 1982 Multiple Regression In Behavioral Research Paper

## EDEP 604: Multiple Regression in Behavioral Research (3 credits)

Advanced applications of general linear model to complex problems of data analysis. Relation of analysis of variance and covariance to regression analysis. Nonlinearity and treatment of missing data. Pre: EDEP 601 and 602, or consent. (Cross-listed as PSY 612 and SW 654)

Modified: April 6, 2006

### Basic Texts:

**Pedhazur, E. J.** (1997). *Multiple regression in behavioral research *(3rd ed.). Orlando, FL: Harcourt Brace.

**Ward, J. H., Jr., & Jennings, E.** (1973). *Introduction to linear models*. [Originally published by Prentice-Hall, now available from The Institute for Job and Occupational Analysis (IJOA), 10010 San Pedro, Suite 440, San Antonio, Texas 78216

### Other References:

**Aiken L & West S.** (1991). *Testing Interactions in Multiple Regression.* Hillsdale NJ: Lawrence Erlbaum.

**Cohen J, Cohen P, Aiken L, & West S.** (2003). *Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences. 3rd ed.* Hillsdale NJ: Lawrence Erlbaum.

**Darlington, R. B.** (1990). *Regression and linear models.* New York: McGraw-Hill.

**Judd, C. M., & McClelland, G. H.** (1989). *Statistical analysis: A model comparison approach.* Orlando, FL: Harcourt Brace Janovich. Their Book; Their Course.

**Pedhazur, E. J., & Schmelkin, L. P.** (1991). *Measurement, design, and analysis: An integrated approach.* Hillsdale, NJ: Elrbaum.

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

### Data Sets and SAS Control Files

### Online Resources: (barely scratch the surface of what's available on the Internet)

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.

#### Relevant Text Online

- Probing Interactions in Multiple Linear Regression, Latent Curve Analysis, and Hierarchical Linear Modeling: Interactive calculation tools for establishing simple intercepts, simple slopes, and regions of significance (Kristopher J. Preacher, Patrick J. Curran, and Daniel J. Bauer University of North Carolina at Chapel Hill)
- A Primer on Interaction Effects in Multiple Linear Regression (Kristopher J. Preacher, University of North Carolina at Chapel Hill)
- Demonstration of the Importance of Centering Continuous Variables Before Creating Interaction Terms (Scot W. McNary) (.pdf)
- James Algina's pages (syllabi, SAS and SPSS code, papers, etc.)
- Advanced Statistics: Manifest Variables Analysis (Stephen Lea, University of Exeter)
- Electronic Statistical Textbook (from StatSoft)
- HyperStat (David M. Lane, Rice University)
- The Little Handbook of Statistics Practice (Gerard E. Dallal, Tufts University)
- Multiple Regression (G. David Garson, North Carolina State University)
- Multivariate Statistics: Concepts, Models, and Applications (David W. Stockburger, Missouri State University)
- Probability Theory -- The Logic of Science (E. T. Jaynes, Washington University – St. Louis)

#### Online Articles

- Behrens, J. T. & Yu, C. H. (1994, June). The visualization of multi-way interactions and higher-order terms in multiple regression. Paper presented at the annual meeting of the Psychometric Society.
- Chow, S. L. (1996). Precis of
*Statistical significance: Rationale, Validity and Utility*. London, Sage. - Jones, L. V. & Tukey, J. W. (2000). A sensible reformulation of the significance test.
*Psychological Methods*,**5**, 411-414. - Laviolette, M. (1994). Linear regression: The computer as a teaching tool.
*Journal of Statistics Education*,**2**(2). - Osborne, J. W., & Waters, E. (2002). Four assumptions of multiple regression that researchers should always test.
*Practical Assessment, Research & Evaluation*,**8**(2). - Smith, B. & Sechrest, L. (1991). Treatment of aptitude by treatment interactions.
*Journal of Consulting and Clinical Psychology*,**59**(2), 233-244. - Walker, M. E. (1999). Commentary on Greenwald et al. (1996). Effect sizes and p values: What should be reported and what should be replicated? In
*Psychophysiology*,**33**, 175-183. (Michael E. Walker, Ohio State University) - Ward, J. H., Jr. & Fountain, R. L. (1996). More problem solving power: Exploiting prediction models and statistical software in a one-semester course.
*Journal of Statistics Education*,**4**(3).

#### Glossaries

- Data Analysis BriefBook (R. K. Bock & W. Krischer, CERN)
- A Glossary of Statistics (Norman Marsh, University of Liverpool)
- Glossary of Terms from
*Educational research: Quantitative, qualitative, and mixed approaches*by Burke Johnson & Larry Christensen - Internet Glossary of Statistical Terms (Howard S. Hoffman, Bryn Mawr College)
- Online Glossaries for Statistics and Econometrics (John Kane, SUNY-Oswego)
- Statistics Glossary (StatSoft)
- Statistics Glossary (Valerie J. Easton & John H. McColl, The STEPS Project)
Statistics Glossary (variant on STEPS Project just above)

- SticiGui: Glossary of Statistical Terms (Philip B. Stark, UC Berkeley)
- SurfStat: Glossary (Keith Dear, Australian National University)

#### Guidelines

#### Calculators and Online Applications

#### Statistical Packages

#### Downloadable Software

- The Comprehensive R Archive Network (CRAN)
- gretl: Gnu Regression, Econometrics and Time-series Library (Allin Cottrell, Wake Forest University)
- Essential Regression: Free Statistical Software for Microsoft Excel (Dave Steppan, Joachim Werner, & Bob Yeater)
- MacAnova (not just for Macs) (Gary W. Oehlert and Christopher Bingham, University of Minnesota)
- Mx (Michael Neale, Virginia Commonwealth University)
- OpenStat (William G. Miller, Iowa State University)
- PQRS (Probability Calculator for the PC)
- |Stat (Gary Perlman, UC San Diego)
- StatCalc (Kalimuthu Krishnamoorthy, University of Louisiana-Lafayette)
- StatLib (Carnegie Mellon University)
- ViSta - The Visual Statistics System (Forrest W. Young, University of North Carolina)

#### Data Set Libraries

#### Courses

#### Discussion Lists

#### General

### Course Outline:

A. Review of Ordinary Least Squares (OLS) and the General Linear Model (GLM)

1. The Measurement Model

2. The Structural Model

B. Review of Coding Schemes for Categorical Variables

1. Dummy coding

2. Contrast coding

C. Null Hypothesis Testing

1. Comparing Nested Models

2. The F-ratio

D. Analysis of Variance, Analysis of Covariance, Multiple Regression, and the GLM

E. GLM and "Non-linear" Relationships

1. Linear and Non-linear Transformations

2. Polynomial Regression

F. Missing Data on Explanatory Variables

G. Categorical Outcome Variables

1. Discriminant Function Analysis (OLS)

2. Maximum Likelihood Estimation

a. Logistic regression

b. Log-linear models

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.

Questions or comments to: daniel@hawaii.edu

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