GEORGE WARREN BROWN SOCIAL OF SOCIAL WORK WASHINGTON UNIVERSITY Ph.D. PROGRAM IN SOCIAL WORK FALL 2010 ADVANCED MULTIVARIATE STATISTICS S90-6901.01 CREDIT HOURS: 3 GRADE: L/G ROOM: Brown 209 TIME: Tues., 1:00 – 3:00 LAB: Tues., 3:15-5:15 pm In Goldfarb 330 TA: Jin Huang TA’S E-MAIL: jhuang22@wustl.edu INSTRUCTOR: David Gillespie OFFICE: Brown 106 OFFICE HOURS: Mon., 9:00 – 11:00 a.m. & by appointment PHONE/VOICE MAIL: 935-6674 E-MAIL: davidg@gwbmail.wustl.edu OR davidfg@fidnet.com TA’S OFFICE: B-05; PHONE: 935-8786 TA’S OFFICE HOURS: Thurs., 1:00 – 3:00 p.m. & by appointment

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COURSE DOMAIN AND BOUNDARIES

This course introduces structural equation modeling (SEM). SEM is a flexible and extensive method for testing theory. Structural equation models are best developed on the basis of substantive theory. The hypothesized theoretical relationships imply particular patterns of covariance. Statistical estimates of these hypothesized covariances indicate within a margin of error how well the models fit with data. The development and testing of these models advances theory by including latent variables, by estimating measurement error, by accepting multiple indicators, by accomodating reciprocal causation, and by estimating model parameters simultaneously. Structural equation models subsume factor analysis, regression, and path analysis. The integration of these traditional types of analysis is an important advancement because it makes possible empirical specification of the linkages between imperfectly measured variables and theoretical constructs of interest.

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COURSE GOALS To increase skill in developing theory that implies testable models of social phenomena. To deepen appreciation of the inseparable integration of research methods and theory construction. To understand useful applications of structural equation models. To know how to fit structural equation models to data. To know how to publish the results of analyses with structural equation models. To have fun with the routines and challenges of structural equation modeling. BOOKS AND MANUALS

Hoyle, Rick H. (Editor). 1995. Structural Equation Modeling: Concepts, Issues, and Applications. Thousand Oaks: Sage. Kline, Rex B. 2010. Principles and Practice of Structural Equation Modeling. Third Edition. New York: Guilford Press. Jöreskog, Karl G. and Sörbom, Dag. 1993. LISREL 8: Structural Equation Modeling with the SIMPLIS Command Language. Hillsdale, NJ: Lawrence Erlbaum Associates. Schumacker, Randall E. and Lomax, Richard G. 2010. A Beginner’s Guide to Structural Equation Modeling. Third Edition. Mahwah, New Jersey: Lawrence Erlbaum Associates, Publishers. IV. ORGANIZATION OF COURSE

Except for August 31 and November 30, the first hour of each class is devoted to discussing the topic introduced and read about during the preceding week. This is followed by a short break. During the second hour, I introduce a new topic. The topics are listed below in section VII beginning at the top of page 4. For example, the topic listed for our first class today is “Multivariate Assumptions and Data Preparation.” After my introducing this topic and your reading more about it during the week, we return to class the next week to spend the first hour clarifying what it is that we understand about multivariate assumptions and data preparation. This pattern – first hour for review and second hour for new material – is used throughout the semester. To help guide class discussion during the first hour, a group of students will take the lead in facilitating the discussion. Each group will have four opportunities during the semester to facilitate our class discussion. The group scheduled to lead the discussion each week prepares an outline of the most important ideas in the reading and also lists questions that would be helpful to address. The schedule for leading class discussions will be established during the first day of class and posted on Blackboard soon after the first class. Facilitating the discussion means encouraging others to talk about what they know and don’t know from the reading and related ideas. Good facilitation makes it possible for everyone to participate in the discussion. The fact a particular group is facilitating our discussions does not reduce the importance of each person each week raising the questions that arise

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in their mind as they do the reading. These questions are usually discussed in class but also are turned in as part of each individual’s written work for the week. The assigned readings include a variety of substantive areas, but of course not all areas are represented. Each person is encouraged to share from their area of interest readings that illustrate particularly well a certain concept or technique, or readings that contribute to learning ideas and techniques useful in structural equation modeling. There is a computer lab associated with this class. The lab meets in room G-330 on Tuesday 3:15-5:15 p.m. The lab instructor is Jin Huang. Exercises are offered each week. Most of these exercises are illustrated during the lab sessions. Questions or comments that arise in between class sessions may be posted through e-mail. My email addresses and Jin’s address are listed in the top section of this syllabus. Responses to questions or comments emailed may be made directly through e-mail to the person that sent the message, or responses may be directed to everyone participating in the course, or responses may be included in a subsequent class discussion. Information about structural equation modeling is available on SEMNET, a listserve group on the Internet. A description of SEMNET is at http://www.gsu.edu/~mkteer/semnet.html. To join this group, send to LISTSERV@BAMA.UA.EDU the command SUB SEMNET FIRST-NAME LAST-NAME. Information from this group may be gathered passively by monitoring the messages or gathered actively by asking questions. Protocol for participation is sent when you join the group. There are many other SEM-related sites on the Internet. Ed Rigdon’s homepage is a good place to start: http://www2.gsu.edu/~mkteer/ V. CRITERIA TO MONITOR LEARNING

A. Questions. This is a set of questions, which if answered help you understand structural equation modeling. You are asked to write one or more of the questions that arise in your mind as you do the reading for each week. We will seek to answer your questions each week. B. Writing. This is a question or exercise to be done out of class. The purpose of these exercises is to help you learn how to apply the concepts and methods of structural equation modeling to your own practice and theory. The writing exercises for each week are listed under the subheading of “Writings” in the course schedule (section VII, pages 4-11). C. Participation. This is your contribution to discussions during class. I encourage active participation because I believe it creates a learning environment that benefits all of us. D. Paper. This is a publishable paper. The only constraint on your paper is that it must include or relate to structural equation modeling. I suggest a few options on page 12 to help you get started in thinking about the kind of paper you want to write. VI. GRADING

A. Weekly questions and writing. Your weekly written work contributes 20% of your final course grade. I consider the interest and generality of the questions raised, the accuracy and parsimony of the exercises.

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B. Participation. Participation in class discussions counts as 30% of your final course grade. I consider the relevance of any questions or comments made to the topic under discussion, content quality, novelty, and value to others. Value to others is represented through the generality of ideas expressed and includes your written outline of ideas from the readings on those occasions when you lead the class discussion. In addition, I also consider your bringing to our attention exemplary readings in your area relevant to any topic we read about or discuss. C. Report. The final paper provides 50% of your course grade. I consider your thoroughness in covering the topic you write about, logical consistency, lack of redundancy, accuracy of reporting, clarity, and creativity. To have your grade recorded for the autumn 2010 semester, I must receive your paper by the last day of class – November 30, 2010. VII. COURSE SCHEDULE: CLASS MEETING DATES, WEEKLY TOPICS, OBJECTIVES, READING, AND WRITTEN ASSIGNMENTS

A. 31 August: Multivariate Assumptions and Data Preparation Objectives 1. To understand the major assumptions of structural equation modeling. 2. To know how to detect violations of the assumptions in structural equation modeling. 3. To know possible solutions to the violations of assumptions in structural equation modeling. Readings Kline, “Data Preparation.” Pp. 46-72. Osborne, “Notes on the use of data transformations.” Pp. 1-10. Schumacker & Lomax, “Introduction.” Pp. 1-10. West, Finch, & Curran, “Structural equation models with nonnormal variables: problems and remedies.” Pp. 56-75 in Hoyle. Writings 1) Write at least one question that you consider important with respect to understanding the assumptions of structural equation modeling. 2) Write a single paragraph that summarizes your area of theoretical interest. List in a column the variables that you believe are essential in developing or testing your theory. 3) Describe how you will screen and summarize the interval or ratio level variables that interest you. If you have access to data report key diagnostic statistics.

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B. 7 September: Theory Construction, Regression, and Causal Models. Objectives 1. To know the criteria of causality. 2. To know the main assumptions of theory construction and causal modeling. 3. To understand distinctions between recursive and non-recursive models. Readings Blalock, Hubert M. 1961. “Introduction.” Pp. 3-26 in Causal Inferences in Nonexperimental Research. Chapel Hill: The University of North Carolina Press. Kline, “Specification Concepts” and “Path Analysis Models.” Pp. 96-111. Schumacker & Lomax, “Regression Models,” and “Path Models.” Pp. 113-137; 138-153. Writings 1) Write at least one question that you consider important with respect to understanding theory construction and causal modeling. 2) Draw a diagram of a model using the variables that you listed last week from your area of theoretical interest. Define each variable in your model. Write a paragraph that describes how the model works. 3) Write three sentences that convey the most important results of a factor analysis, multiple regression or path analysis. If you have access to data conduct a factor analysis, multiple regression, or path analysis. C. 14 September: Overview of Structural Equation Modeling (SEM) Objectives 1. To understand SEM as an extension of the general linear model, and recognize this extension as a fundamental advancement in our capability to construct theory. 2. To know the steps in constructing structural equation models. 3. To know appropriate applications of regression, measurement models (factor analysis), correlation, multiple regression, “bivariate” regression, path analysis, MIMIC models, and structural equation models. Readings Hoyle, “The Structural Equation Modeling Approach: Basic Concepts and Fundamental Issues.” Pp. 1-15. Jöreskog & Sörbom, “Simple examples.” Pp. 1-50. Kline, “Introduction.” Pp. 3-18; and “Steps of SEM.” Pp. 91-95. Schumacker & Lomax, “SEM Basics.” Pp. 57-71.

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Writings 1) Write at least one question that you consider important with respect to understanding structural equation modeling. 2) Revise the diagram drawn last week using the graphic conventions described in Joreskog and Sorbom (1993) or Schumacker and Lomax (1996). Again, define each variable, and write a paragraph that describes any changes in how the model works. 3) Use an SEM program to estimate a model. D. 21 September: Establishing Model Identification Objectives 1. To understand the role of identification in theory construction. 2. To know how to recognize likely cases of underidentification, exact identification, and overidentification. 3. To know what to do if a model is underidentified. Readings Kline, “Identification.” Pp. 124-148. MacCallum, Robert C. 1995. “Model specification: procedures, strategies, and related issues.” Pp. 16-36 in Hoyle. Wothke, “Nonpositive definite matrices in structural modeling.” Pp. 256-293 in Bollen & Long (Eds.), Testing Structural Equation Models. Sage, 1993. Writings 1) Write at least one question that you consider important with respect to understanding identification. 2) Label all parameters of a graphic model derived from your theory or area of interest. Distinguish the parameters that will be estimated. Note the degrees of freedom in your model. 3) Select a model to test. Demonstrate that the model is identified. Test the model and comment briefly on the results. E. 28 September: Procedures and Criteria for Estimating Models Objectives 1. To know estimation procedures and the criteria for judging them. 2. To know the main assumptions and characteristics of fitting functions. 3. To understand the idea of asymptotic properties.

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Readings Jöreskog, Karl G. 1990. “New developments in LISREL: Analysis of ordinal variables using polychoric correlations and weighted least squares.” Quality and Quantity 24: 387404. Kline, “Estimation.” Pp. 154-182. Kennedy, Peter. 1992. “Criteria for estimators.” Pp. 9-41 in Kennedy, A Guide to Econometrics. Third Edition, Cambridge, Massachusetts: MIT Press. Writings 1) Write at least one question that you consider important with respect to understanding estimation. 2) Discuss the role of estimation in developing your theory. 3) Test a structural equation model using maximum likelihood estimation. Re-estimate the same model using one other estimation procedure. Outline similarities and differences between the parameter estimates. F. 5 October: Testing How Well Models Fit Data Objectives 1. To understand the logic of testing models. 2. To know how to interpret indices of misfit and goodness-of-fit. 3. To appreciate the strengths and limitations of statistical tests in constructing theory. Readings Hu & Bentler, “Evaluating Model Fit.” Pp. 76-99 in Hoyle. Jöreskog & Sörbom, “Path diagrams;” “Fitting and testing.” Pp. 85-131. Kline, “Hypothesis Testing.” Pp. 189-209. Schumacker & Lomax, “Model Fit.” Pp. 72-112. Writings 1) Write at least one question that you consider important with respect to understanding tests of model fit. 2) Discuss the fit criteria that are most appropriate for the model that currently represents your theory. 3) Test a structural equation model. Based on your results, outline what must be done next to improve the model or theory that implied the model.

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G. 12 October: Assessing the Validity of Observed and Latent Variables Objectives 1. To know the difference between exploratory and confirmatory factor analysis. 2. To understand alternative conceptions of validity. 3. To understand applications of cause and effect indicators. Readings Bollen, Kenneth & Lennox, Richard. 1991. “Conventional wisdom on measurement: A structural equation perspective.” Psychological Bulletin, 110(2), 305-314. [CM] Kline, “Measurement Models and Confirmatory Factor Analysis.” Pp. 230-261. Schumacker & Lomax, “Confirmatory Factor Models.” Pp. 154-181. Writings 1) Write at least one question that you consider important with respect to understanding validity. 2) Describe the measurement model for a concept in your theory. 3) Estimate a confirmatory factor analysis model. Comment on the model’s validity. H. 19 October: Assessing the Reliability of Observed and Latent Variables Objectives 1. To understand the consequences of measurement error. 2. To know how to model multiple indicators. 2. To know applications of parallel, tau-equivalent, and congeneric models of reliability. Readings Bollen, Kenneth. 1989. “Reliability.” Pp. 206-223 in Kenneth A. Bollen, Structural Equations with Latent Variables. New York: John Wiley & Sons. Miller, Michael B. 1995. “Coefficient Alpha: A Basic Introduction From the Perspective of Classical Test Theory and Structural Equation Modeling.” Structural Equation Modeling 2 (3): 255-273. Rigdon, Edward E. 1994. “Demonstrating the Effects of Unmodeled Random Measurement Error.” Structural Equation Modeling 1 (4): 375-380. Writings 1) Write at least one question that you consider important with respect to understanding reliability. 2) Describe how you will assess reliability of the measures used in your theory. 3) Estimate a model with measures that assume perfect reliability. Re-estimate the model allowing for measurement error. Compare results and comment on any differences.

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I. 26 October: Working with Ordinal Data Objectives 1. To understand applications of polychoric, polyserial, and tetrachoric correlation matrices. 2. To understand how to apply the WLS estimation procedures. 3. To know the limitations of working with ordinal data. Readings Aish, Anne-Marie & Jöreskog, Karl G. 1990. “A panel model for political efficacy and responsiveness: An application of LISREL 7 with weighted least squares.” Quality and Quantity 24: 405-426. Jöreskog, Karl G. & Sorbom, Dag. 1993. “Analysis of ordinal and other non-normal variables.” Pp. 223-224 in LISREL 8: User's Reference Guide. Chicago: Scientific Software. Mitchell, Joel. 1986. “Measurement scales and statistics: a clash of paradigms.” Psychological Bulletin 100(3): 398-407. Writings 1) Write at least one question that you consider important with respect to understanding the use of ordinal data in structural equation modeling. 2) Discuss the implications of including one or more ordinal variables in models implied by your theory. What needs to be done to improve the precision of the ordinal variable(s)? 3) Estimate a model that includes one or more ordinal variables. Indicate the assumptions you made regarding the ordinal variables. Test one of your assumptions. J. 2 November: Estimating Stacked or Multiple Group Models Objectives 1. To know how to test conditional hypotheses. 2. To understand the advantages of stacked models over separate analyses of comparable models for different sets of cases. 3. To know how to test whether differences between groups are due to measurement or structural parameters. Readings Joreskog & Sorbom. “Multi-Sample Examples.” Pp. 51-61. Kline, “Interaction Effects and Multiple-Sample SEM.” Pp. 327-354. Schumacker & Lomax. “Multiple-Sample Models.” Pp. 240-250. Schumacker, “Latent Variable Interaction Modeling,” Pp. 40-54.

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Writings 1) Write at least one question that you consider important with respect to understanding stacked models. 2) Discuss a stacked model implied by your theory. How does this approach differ from traditional analyses? 3) Estimate a stacked model. Explain your logic for testing the hypotheses in this model. Indicate at least one assumption of the model that you are not testing and comment on how this assumption could affect your results. K. 9 November: Estimating Models with Time Series Data and Correlated Error Objectives 1. To understand the advantages of modeling with time-series data. 2. To know how to test a model using time-series data. 3. To understand different kinds of correlated error. Readings Gollob, Harry F. & Reichardt, Charles S. 1987. “Taking account of time lags in causal models.” Child Development 58 (No. 1): 80-92. Kline, “Mean Structures and Latent Growth Models.” Pp. 299-325. Rubio, Doris M. and Gillespie, David F. 1995. “Problems with error in structural equation models.” Structural Equation Modeling 2(4): 367-378. Writings 1) Write at least one question that you consider important with respect to understanding time-series and correlated error in structural equation models. 2) Discuss the time lags involved with one or more relationships in your theory. 3) Fit a model to time series data, or use correlated error to illustrate specification error in a cross-sectional model. L. 16 November: Assessing Mediation and Alternative Models Objectives 1. To understand the value of conceptualizing and testing alternative models. 2. To know how to develop nested models. 3. To understand how to interpret mediation effects.

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Readings Brown, Roger L. 1997. “Assessing Specific Mediational Effects in Complex Theoretical Models.” Structural Equation Modeling 4 (2): 142-156. Mulaik & James. “Objectivity and Reasoning in Science and Structural Equation Modeling,” Pp. 118-137 in Rick H. Hoyle. Writings 1) Write at least one question that you consider important with respect to understanding mediation and alternative models. 2) Describe alternative possibilities for one or more mediating variables in a model implied by your theory. 3) Estimate a model with a mediating variable. Write one paragraph that interprets your results. M. 23 November: Guidelines for Publishing SEM Results Objectives 1. To know the main theoretical, statistical, and practical points to include in writing up results for publication. 2. To know which statistics to report for different kinds of SEM models. 3. To know how to construct tables and graphs that highlight the most important results for different kinds of models. Readings Guo, Perron & Gillespie, “A systematic review of structural equation modeling in social work research.” British Journal of Social Work (Advance Access), Pp. 1-19. Hoyle & Panter, “Writing about structural equation models.” Pp. 158-176. Kline, “How to Fool Yourself with SEM.” Pp. 356-366. Mueller, Ralph O. 1997. “Structural Equation Modeling: Back to Basics.”Structural Equation Modeling 4 (4): 353-369. Schumacker & Lomax, “Reporting SEM Research.” Pp. 213-239. Writings 1) Indicate the journal that you intend to submit an article to first, and describe your reason for selecting this particular journal. 2) Design one or more tables to show the results from testing a structural equation model.

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N. 30 November: Presenting Final Papers Objectives 1. To know how to present succinctly your theory and representative models that can be or have been tested. Possible Options for Final Paper 1) Replicate and extend a multiple regression or path model reported in the literature. Possible extensions include specifying latent variables and structural parameters, incorporating measurement error or modifying the amount of measurement error, assessing validity, assessing reliability, adding or removing particular hypotheses, and using alternative estimation procedures. 2) Use your own data to estimate a theoretically derived model. The model may be a measurement model, full model, or a combination of both. It is not necessary for the model to be original. 3) Explain an issue in the use of structural equation modeling. Any issue discussed in class or raised in the literature is acceptable. Possible issues include model misspecification, twostep procedure to model development, violation of model assumptions, nested models, fit measures, model identification, estimation, correlated error, cause indicators, multiple groups, cross-validation, modification indices, interaction, and ordinal variables. 4) Using the guidelines and assumptions of structural equation modeling, specify a theory in your area of interest and discuss how models derived from the theory will be tested. 5) Taking a particular concept or area of research, compare a structural equation modeling approach with a traditional approach. An alternative expression of this option would be to discuss how a concept or area of research has been changed through applications of structural equation modeling.

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