Multivariate Analysis in Educational Research Course Syllabus Fall 2012 Education Y604 Section 17348 Tuesday & Thursday: 11:15 AM 12:30 PM Room: ED 3275 LAB.: Tuesday 9:30-10:30 AM, ED 2015 Instructor Ginette Delandshere W.W.Wright Building, 4038 Telephone: 856-8347 gdelands@indiana.edu Graduate Teaching Assistant Meihua Qian W. W. Wright Building mqian@umail.iu.edu Prerequisites Students enrolled in the course should have completed Y502 or its equivalent (Y603 also recommended). Some knowledge of data analysis software (e.g., SAS, SPSS) is also recommended. Course Content This course is based on the premise that the function of statistics is to formulate arguments for explaining comparative differences and relationships or patterns in data. This course focuses on the General Linear Model (GLM) and its extensions, and the various forms it takes in the multivariate context. The forms of the model will be discussed in relationship to the particular research questions for which they are appropriate. A range of multivariate statistical analysis procedures are considered to examine relationships between multiple variables (e.g., multiple dependent and/or independent variables) and comparisons will be made to their univariate equivalent. Principal component and factor analysis will also be covered as a way to reduce the number of measured variables to a smaller number of scores and to study the structure in data or underlying factors. Confirmatory factor analysis and the testing of simple structural models will also be introduced as well as structural equation modeling which allows for the examination of multiple relationships among variables and for taking into account measurement error (using measurement models for latent variables). The limitations (i.e., assumptions) and unresolved issues of each forms of the GLM will be examined. Students will learn to formulate research questions, to select appropriate analysis procedures, to conduct statistical analyses, and to report, interpret and write up narratives of the results in relation to the research questions and context. Y604 Multivariate Statistics Fall 2012 Page 1
Objectives 1. To understand the nature and function of multivariate statistics and to use appropriate procedures to answer specific research questions 2. To carry out statistical analyses and to verify the underlying assumptions 3. To interpret and write up results of statistical analyses in relation to specific research questions and contexts. Textbooks Tabacknick, B. G. & Fidell, L. S. (2013). Using Multivariate Statistics, Sixth Edition. Upper Saddle River, NJ: Pearson Education, Inc. http://wps.ablongman.com/ab_tabachnick_multistats_6/ [T&F] Course notes and materials are also made available for each class session on Oncourse: https://oncourse.iu.edu/portal Some Related Classics Namboodiri, K. Matrix Algebra, An Introduction #38, Beverly Hills, CA: Sage Publications, Inc. Lewis-Beck, M.S. (1980). Applied Regression, An Introduction #22, Beverly Hills, CA: Sage Publications, Inc. Berry, W.D. & Feldman, S. (1985). Multiple Regression in Practice #50, Beverly Hills, CA: Bray, J.H. & Maxwell, S.E. (1985). Multivariate Analysis of Variance #54, Beverly Hills, CA: Klecka, W.R. (1980). Discriminant Analysis #19, Beverly Hills, CA: Kim, J-O. & Mueller, C. W. (1978). Introduction to Factor Analysis #13, Beverly Hills, CA: Kim, J-O. & Mueller, C. W. (1978). Factor Analysis: Statistical Methods and Practical Issues #14, Beverly Hills, CA: Long, S. Confirmatory Factor Analysis, A Preface to LISREL #33. Beverly Hills, CA: Sage Publications, Inc. Y604 Multivariate Statistics Fall 2012 Page 2
Long, S. Covariance Structure Models, An Introduction to LISREL #34. Beverly Hills, CA: Additional References Books Abelson, R. P. (1995). Statistics as Principled Argument. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc. Afifi, A. A., Clark, V. & May, S. (2004). Computer-Aided Multivariate Analysis (4th Edition). Publisher: Chapman & Hall/CRC Byrne, B. (1998). Structural quation Modeling With Lisrel, Prelis, and Simplis: Basic Concepts, Applications, and Programming. Mahwah, NJ: Lawrence Erlbaum Associates, Inc. Byrne, B. (2010). Structural Equation Modeling With AMOS: Basic Concepts, Applications, and Programming (2 nd. Ed.). New York, NY: Routledge, Taylor & Francis Group. Byrne, B. (2011). Structural Equation Modeling with MPlus: Basic Concepts, Applications, and Programming. New York, NY: Routledge, Taylor & Francis Group. Cooley, W. W. and Lohnes, P. R. (1985). Multivariate Data Analysis (2nd. ed.) New York, NY: John Wiley and Sons, Inc. Everitt, B. and Hothorn, T. (2011). An introduction to applied multivariate analysis with R. New York, NY: Springer. Grimm, L. G. and Yarnold, P. R. (2000). Reading and Understanding More Multivariate Statistics. DC: American Psychological Association. Hair, J. F., Black, B., Babin, B. and Anderson, R.E., (2009). Multivariate Data Analysis, (7th. ed.), Macmillan Publishing Company, New York, NY. Harlow, L. L. (2010). The essence of multivariate thinking: Basic Themes and Methods. Mahwah, NJ: Lawrence Erlbaum Associates, Inc. Harris, R.J. (2001). A Primer of Multivariate Statistics, (3rd. ed.), Orlando, FL., Academic Press. Johnson, R. A. & Wichern, D. W. (2007) Applied multivariate statistical analysis. (6th ed.) Y604 Multivariate Statistics Fall 2012 Page 3
Loehlin, J. C. (1992). Latent Variable Models: An Introduction to Factor, Path and Structural Analysis. (2nd. ed.), Hillsdale, NJ: Lawrence Erlbaum Associates, Inc. Morrison, D. F. (2005). Multivariate Statistical Methods, (4th. ed.), Belmont, CA: Brooks/Cole Pedhazur, E.J. (1997). Multiple Regression in Behavioral Research: Explanation and Prediction, Third Edition. Fort Worth : Harcourt Brace College Publishers. Pedhazur, E. J. and Schmelkin, L. (1991). Measurement, Design, and Analysis: An Integrated Approach, Hillsdale, NJ: Lawrence Erlbaum Associates, Inc. Porter, T. M. (1995). Trust in Numbers: The Pursuit of Objectivity in Science and Public Life. Princeton, NJ: Princeton University Press. Stevens, J. (2009). Applied Multivariate Statistics for the Social Sciences, (5th. ed.), Hillsdale, NJ: Lawrence Erlbaum Associates, Inc. Articles/Chapters Brooks, S. P. (2003). Bayesian computations: A statistical revolution. Philosophical Transactions, 361, 2681-2697. Fabrigar, L. R., Wegener, D., MacCallum, R. C., and Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272-299. Huberty, C. J. & Morris, J. D. (1989). Multivariate analysis versus multiple univariate analyses. Psychological Bulletin, 105(2), 302-308. Hox, J. J. & Bechger, T. M. (1998). An introduction to structural equation modeling. Family Science Review, 11(4), 354-373. Kluve, J. (2004). On the role of counterfactuals in inferring causal effects. Foundation of Science, 9, 65-101. Lindley, D. V. (2000). The philosophy of statistics. The Statistician, 49(3), 293-337. Shvyrkov, V. & Persidsky, A. (1991). The importance of being earnest in statistics. Quality and Quantity, 25, 19-28. Wilkinson, L.et, al. (1999). Statistical methods in psychology journals. American Psychologist, 54(8), 594-604. Y604 Multivariate Statistics Fall 2012 Page 4
Tentative Course Outline and Schedule Week 1 Introduction and Overview 8/21-8/23 Students inventory of interests and experience with research, statistics and measurement Taxonomy of Multivariate Techniques Review of univariate analysis techniques Assumptions underlying multivariate techniques Readings: [T&F: Cursive Reading of Chap. 1 & 2] (You can also review the concepts you have learned about bivariate and univariate statistics in Chap. 3) Weeks 2-3 8/28 Making Claims with Statistics & Quantification Function of Statistics Meaning of Measurement [Abelson: Chap.1] [Porter: Chap.4] 8/30 Matrix Algebra 9/4-6 Operations, Order, Trace, Determinant Sums of Square and Cross-Product (SSCP) Inverse, Rank, Eigen Values, Eigen Vectors Readings: [T&F: Appendix A] Weeks 4-6 Multiple Regression 9/11-13 Basic OLS model, assumptions, errors, hypothesis testing 9/18-20 Analysis of the residuals 9/25-27 Outliers, Multicollinearity Types of Multiple Regression Dummy Coding Readings: [T&F: Chap. 4 & 5] _REGRESSION ASSIGNMENT_ Weeks 7-8 Hotelling's T 2 and Manova 10/2-4 Readings: [T&F: Chap. 7] 10/9-11 Weeks 9-10 Discriminant Analysis 10/16-18 Readings: [T&F: Chap. 9] 10/23-25 _EXAMINATION #1_ Y604 Multivariate Statistics Fall 2012 Page 5
Weeks 11-12 Principal Component and Exploratory Factor Analysis 10/30-11/1 11/6-8 Readings: [T&F: Chap. 13] _EFA ASSIGNMENT_ Weeks 13-15 Structural Equation Modeling 11/13-15 Confirmatory Factor Analysis 11/27-29 Covariance Structure Models 12/4-6 Readings: [T&F: Chap. 14] Week 16 _EXAMINATION #2_ Course Assignments and Evaluation I expect all assigned readings to be done as specified for each session. Readings are assigned to complement in-class presentations and discussions, and to formalize understanding of the material. As an enrolled student, you will complete two written assignments, and two examinations. The assignments are designed to evaluate your conceptual understanding of the statistical analysis procedures, their assumptions, the computations involved, how the analyses relate to the research questions as well as the nature of the interpretations and inferences made based on the analysis of data. Short homework (e.g., matrix algebra exercises, reading research articles) will also be assigned for some of the topics and will have to be turned in on a timely basis. Each assignment will be evaluated according to a set of criteria that will be communicated as part of the assignment. The assignments, homework, and examinations will contribute to the final grade as follows: Regression assignment: 20% EFA assignment 20% Examination #1 30% Examination #2 30% Students are also responsible for the assigned readings and for in-class exercises, quizzes and homework assignments. The homework and quizzes will not be graded; they will be checked for completion and adequacy and feedback will be provided. To receive full credit all homework assignments have to be completed and turned in on time. If homework is not turned in or is systematically late, incomplete or inadequate your final grade will be decreased by one grade level or two (e.g., A will turn into A - or B + ) depending on the number of late and incomplete assignments. Grading procedures are in accordance with the Bulletin for the Graduate Program of the School of Education. A course grade of Incomplete will not be assigned except in the case of illness or other emergencies. Intended or unintended cheating and/or plagiarism (see academic handbook) will yield a grade of F in the course. Y604 Multivariate Statistics Fall 2012 Page 6
Grading Scale 91 and above A 78-79 C+ 89-90 A- 72-77 C 87-88 B+ 70-71 C- 82-86 B 68-69 D+ 80-81 B- 62-67 D Other Guidelines for the Course Students are encouraged to discuss the course material among themselves and to assist each other with data analysis. The written part of the assignments should, however, reflect individual student's work. Labs are designed to provide additional assistance to students and include: (1) assistance in setting up computer programs, (2) assistance with homework and assignments, and (3) review of concepts and procedures. Students should come to lab prepared to ask questions. Y604 Multivariate Statistics Fall 2012 Page 7