Course: MK 920...Seminar in Marketing (Structural Equation Modeling) . . . Fall 1996 . . . Computer Number 2782.
Class Meets: T-T 1:15--3:30 PM, Marketing Conference Room (13th Floor), Bus. Admin. Bldg. Final exam due 5 PM on Tuesday, December 3. Depending on class size, we may move--but that may require a change in time, as well. Even if we stay in that room, two classes (Sept. 26 and Oct. 15) will be moved to the Business Communication conference room, down the hall, due to conflicts.
Instructor: Edward Rigdon, 1338 Bus. Admin. Bldg., (404) 651-4180. Office Hours: by appointment only. The best days to find me in my office with time to talk are Monday, Wednesday and Friday.
Text: Bollen, Kenneth A. (1989), Structural Equations with Latent Variables, New York: Wiley. Jöreskog, Karl G., and Dag Sörbom (1989), LISREL 7: A Guide to the Program and Applications (2nd ed.), Chicago: SPSS, Inc. Rigdon, Edward E., and others (1996), The SEMNET FAQ, a World Wide Web site at address http://www.gsu.edu/~mkteer/semfaq.html
Prerequisites: Doctoral standing; familiarity with multivariate statistical methods; an interest in theory-building research.
Warning: All statements in this syllabus are tentative and subject to change. The student is responsible for staying informed of all changes.
To provide feedback about the course, or to get current information about it, access my Web site at "http://www.gsu.edu/~mkteer/mk920.html". I encourage you to "visit" this site regularly, and to become more familiar with the Internet in general. In particular, I encourage you to monitor the traffic on SEMNET (http://www.gsu.edu/~mkteer/SEMNET.html).
Objectives: This course is designed for faculty and doctoral-level students who need a significant familiarity with those statistical techniques known collectively as "structural equation modeling," "causal modeling," or "analysis of covariance structures." The primary objective of this class is to give students (1) the ability to recognize situations where these techniques may be useful in research; (2) an appreciation for the roles of sound theory and sound measurement in making these techniques useful; (3) an understanding of the limitations of these methods; (4) the ability to use available software in conducting research; and (5), the ability to critique the use of these techniques in published research.
Grades: The student's course grade will be based on the following components:
Exam I 20% Exam II 20% Homework and Class Participation 20% Individual Project 40%
EXAMS--There will be one mid-course exam and a final exam, each consisting of essay-type questions. These questions will probe both for understanding of the assigned material and technical ability. Both exams are take-home. Students may consult whatever notes or printed sources they wish, but should document their sources carefully.
HOMEWORK--Homework problems will involve conducting analyses using LISREL and related computer programs. We will aim for at least one problem per week.
PROJECT--Given the diversity of students taking this course, I am willing to negotiate project structure with each student individually. The standard project in this class is to choose a published paper which employed "structural equation modeling" (SEM) methods and conduct a detailed critique. The published study need not have employed the LISREL software, although that would make the task easier. The student's report will begin with a recapitulation and discussion of the theoretical rationale of the published paper in the context of other work in the field, and will discuss why the use of structural equation modeling to test that theoretical model is either appropriate or inappropriate. Students will also examine the properties and development of the measures used in the paper. Students will then attempt to reproduce the SEM analysis undertaken in the article, will try to understand why a particular approach was chosen, will look at weaknesses and limitations of the analysis, and will suggest and evaluate alternatives to the published analysis. Since students will begin this course with relatively little exposure to this field, they should be advised now that the field is filled with misconceptions and is rapidly changing, so the publication status of a paper that uses these methods is no guide to the quality of analysis in the paper.
Students need to identify the paper to be critiqued as early as possible. Students should give a copy of this paper to their instructor, who will either approve or disapprove the project. Papers may be disapproved either because of inappropriateness for this course--too simple, too complex, or too little information in the article--or because of apparent reporting problems in the paper.
To represent a sufficient challenge, the model being reproduced must have at least 4 latent constructs and at least 10 measures. The article must include the covariance or correlation matrix used in the original analysis--otherwise, the analysis cannot be reproduced.
As an alternative, students may analyze data previously collected by the student. However, I am not likely to approve projects that hinge on data or other resources that are not available at the beginning of the quarter.
Attendance: Naturally, students will be expected to attend and participate in all class sessions. It would be silly for someone to take this class who did not expect to participate fully.
TENTATIVE LESSON PLAN--MK 920
SEMINAR IN MARKETING
Sept. 24 . . . Class 1: Introduction to Class
This class needs to (1) introduce everyone to each other, (2) introduce everyone to the class' requirements, objectives and style, (3) build the proper mindset for studying this technique, and (4) survey the basic rationale underlying SEM.
Sept. 26 . . . Class 2: Basics 1--model elements/variance and covariance algebra
This class will begin with an introduction to the various elements that appear in structural equation models. Then we will look at one of the most important mathematical tools for understanding this method--the algebra of variances and covariances. This tool will help students to understand how the method should behave under well-specified conditions--so that the computer programs will not be a complete "black box."
Reading: Bollen (1989), ch. 2. (Ch. 1 features some interesting historical notes.)
Leading questions: (1) How do you pronounce the following Greek characters: , , , , , ? (2) What are the eight parameter matrices in the general LISREL model (hint: not all Greek characters represent parameters)? (3) Suppose that x = a * + and y = b * + c * , and suppose that and are known to be uncorrelated with and --what is the covariance between x and y? (4) Since structural equation modeling works with covariances rather than the raw data itself, what is the role of pre-analysis data scanning in this method?
Oct. 1 . . . Class 3: Basics 2--matrix algebra
SEM is best understood from a matrix perspective. This class will refresh students' grounding in matrix algebra. We will work many examples, and begin to see how matrix algebra concepts pervade this method. Students particularly need to master the following matrix concepts: addition and subtraction, multiplication, transposition, determinants and inverses, and how the inverse is used in place of matrix division.
Reading: Matrix algebra chapters to be assigned,
Leading questions: (1) If A is a 3 x 3 matrix of 2's, and I is a 3 x 3 identity matrix, what is
(A + I) and what is A * I? (2) If X is a data matrix, with one row per case, and each column representing a variable, what is X' * X? (3) What does it mean when a matrix is "not positive definite," and what does it imply about other operations that may be performed on such a matrix? (4) What is the determinant of a 3 x 3 matrix whose first row is (3 -1 7), whose second row is (0 3 2), and whose third row is (2 -3 1), what is its inverse, and what is the determinant of the inverse? (4) Given the equation Y = X * B + Z, where B is a vector of parameters, and the assumption that cov (X, Z) = 0, and assuming that all matrices are conformable for these operations, derive the matrix formula for B, which is B = (X'X)-1(X'Y).
Oct. 3 . . . Class 4: Looking at a LISREL printout
We'll look at a printout from a LISREL run. We'll see how we got from a path diagram to a mathematical model. I'll talk about a systematic approach to examining a LISREL printout, which may optimize efficiency and minimize frustration.
Reading: Jöreskog and Sörbom (1989), ch. 1. Sample LISREL printout. Cronin and Taylor (1992) . . .
Leading questions: (1) Looking at a LISREL printout, how can you tell if you set up the problem as you intended? (2) Based on the printout, what are two ways you can determine the number of parameters that the model is estimating? (3) How do you read a stem-leaf diagram? (4) Where can you see the total effects of a given exogenous (independent) construct on a given endogenous (dependent) construct?
Oct. 8 . . . Class 5: LISREL program lines
The aim of this class is to get students using the program as soon as possible. Statistical programs, especially in their early years, tend to be confusing and hard to use. LISREL 7 includes many command options, some of which can make using the program much less tedious, and make input and output files much easier to read. After students have these basics, we'll start running LISREL problems.
A LISREL problem will be assigned.
Reading: Jöreskog and Sörbom (1989), ch. 2.
Leading questions: (1) How many different ways can you find to specify that the parameters in a given matrix are free to be estimated? (2) What are the order requirements for different program lines--that is, which lines must be where, relative to other lines? (3) Suppose you specify at one point that a certain parameter is free, but at another point specify that it is fixed--which specification takes precedence? (4) LISREL wants the covariance matrix sorted so that the Y variables come first, followed by the X variables. Suppose your covariance matrix is arranged in a different order--what can you do?
Oct. 10 . . . Class 6: "Observed variable" models
One mark of true understanding of a method is the ability to relate that method to other methods. Plus, this sort of question often shows up on field exams. This class should give students the ability to show that, indeed, regression and analysis of variance are merely special cases of the general structural equation model. To demonstrate this, we'll see how to specify those other models using LISREL. This ability will lead naturally into the question of when researchers should break away from the special cases to use the more general method.
This class will also include a review of two key problems in modeling--multicollinearity and missing predictors.
A LISREL problem will be assigned.
Reading: Jöreskog and Sörbom (1989), ch. 4. We'll take a close look at Jöreskog's Examples 4.2 and 4.3. After this class, students will be assigned the task of setting up and running those examples, using the GLS fitting function.
Leading questions: (1) Can you demonstrate clearly the relationship between regression and Anova/Ancova, and the relationship of those techniques to structural equation modeling? (2) Can you tell your dissertation committee when you should use LISREL and when you should use other linear modeling tools?
Oct. 15 . . . Class 7: Measurement Error
Bollen makes the "well-known" point that unrecognized measurement error in the predictor variables causes negative bias in parameters, with other potential effects depending on the correlation of predictors. We'll see some additional effects of ignoring random measurement error in the Fergusson and Horwood (1984) data.
Reading: Bollen (1989), ch. 5; Fergusson and Horwood (1984), "Life Events and Depression in Women: A Structural Equation Model," Psychological Medicine, 14, 881-89; Rigdon (1994), "Demonstrating the Effects of Unmodeled Random Measurement Error," Structural Equation Modeling, 1, 375-80. Students should work on finding the pieces of information in the Fergusson and Horwood paper that would be necessary to replicate their analysis.
Leading questions: (1) When can researchers ignore the potential for random measurement error? (2) How can researchers use the results of a LISREL analysis to detect the possible presence of measurement error?
Oct. 17 . . . Class 8: The LISREL Measurement Model
One of the strengths of structural equation modeling is its ability to incorporate factor-analytic measurement models. We'll review basic concepts in measurement and see how they relate to the elements of a LISREL analysis. We'll also look at the distinctions between factor analysis (the measurement model used in LISREL) and a competing model, principle component analysis.
Reading: Bollen (1989), ch. 6; Jöreskog (working paper), "Basic Ideas of Factor and Component Analysis." Another homework assignment will be made.
Leading questions: (1) What are four differences between exploratory factor analysis and principle components analysis? (2) How can you evaluate the validity of measures using a LISREL printout? How about reliability?
Oct. 22 . . . Class 9: The full LISREL model--Practicum and Review
It's time to review everything we've learned about this method. Also, let's practice reproducing a LISREL analysis from a published article. The article is Hallen, Johanson and Seyed-Mohamed (1991). Warning: if you estimate their model, as described in the paper, you will not get their result. A correct reproduction of their model should yield a 2 of about 74, with 39 degrees of freedom. Set AD=OFF on the OUtput line. Look for evidence of fit problems, and ask yourself how the authors obtained the results that they reported.
Reading: Rigdon (1994), "Calculating Degrees of Freedom for a Structural Equation Model," Structural Equation Modeling, 1, 274-78; Hallen, Johanson and Seyed-Mohamed (1991), "Interfirm Adaptation in Business Relationships," Journal of Marketing, 55 (April), 29-37.
Leading questions: Please bring your own questions to this class. Let's eliminate lingering misunderstandings now. The main question that I have for you is, (1) Suppose you suspect that a term is correlated with an term--how can you check this possibility in a LISREL printout?
Oct. 24 . . . Class 10: Identification
We cannot estimate all models that might be of theoretical interest. In particular, we cannot estimate models that are not "identified." We will look at ways to tell whether or not a given model is identified, and talk about some very recent developments.
Reading: Bollen (1989), pp. 88-104, 238-54, 326-33; Rigdon (1995), "A Necessary and Sufficient Identification Rule for Structural Models Estimated in Practice," Multivariate Behavioral Research.
Leading questions: (1) How many measures do we need in order to estimate a one-factor model? A two-factor model? (2) Can we "eyeball" a model and tell whether or not it is identified? (3) If our model of interest is not identified, what can we do?
Oct. 29 . . . Class 11: The full LISREL model--Second Practicum
The point of this class is to let students apply what they have learned, including clarifications from the first practicum, to a re-analysis of a second published article. This will also be an open floor for questions. Note that in reproducing the Lichtenstein, Bloch and Black model, you should get results that are close to those reported in the paper, although that analysis was performed with LISREL VI.
Reading: Lichtenstein, Bloch and Black (1988), "Correlates of Price Acceptability," Journal of Consumer Research, 15 (September), 243-252.
Leading question: How do you interpret the fit evidence for this model in light of our discussion of measure development?
Oct. 31 . . . Class 12: Fit Assessment and Fit Indices in Structural Equation Modeling
What is the proper role of fit assessment and hypothesis testing in structural equation modeling? We'll talk about both "traditional" and newer fit indices.
Readings: Bollen (1989), pp. 256-96; Bentler (1990), "Comparative Fit Indexes in Structural Models." Psychological Bulletin, 107, 238-46; Browne and Cudeck (1992), "Alternative Ways of Assessing Model Fit," Sociological Methods and Research, 21 (2), pp. 230-58. Be warned--this is some tough sledding.
Nov. 5 . . . Class 13: Fit Assessment II--Nested Model Strategies
The "traditional" approach to model fit addresses the question, "Does this model fit?" But more and more, researchers ask, "Which of these several models fits the best?" And you can't necessarily answer the question the same way. These readings provide a classical approach to this problem.
Reading: Bollen (1989), pp. 289-304; Anderson and Gerbing (1988), "Structural Equation Modeling in Practice: A Review and Recommended Two-Step Approach," Psychological Bulletin, 103 (3), 411-23.
multiple groups here??
Nov. 7 . . . Class 14: Multi-Sample Analysis
We'll talk about the analytical opportunities in comparing model fits and parameter estimates across data samples taken from different groups. We'll also talk, finally, about the long-ignored means of latent variables, and how we can estimate them. This discussion will touch on ways to include interaction effects in structural equation models.
Readings: Jöreskog and Sörbom (1989), ch. 9, 10; Vandenberg and Scarpello (1990), "The Matching Model: An Examination of the Processes Underlying Realistic Job Previews," Journal of Applied Psychology, 75, 60-67; Mackenzie and Spreng (1992), How Does Motivation Moderate the Impact of Central and Peripheral Processing on Brand Attitudes and Intentions?" Journal of Consumer Research, 18, 519-29.
Leading questions: (1) What is the potential impact of sample size on Vandenberg and Scarpello's findings regarding the fit of the model to the different groups? (2) How are degrees of freedom calculated for the Mackenzie and Spreng model? (3) When is it important to include mean effects in a structural equation model?
Nov. 12 . . . Class 15: Causality and "Causal" Modeling
It is a trivial point that structural equation modeling, which is also unfortunately known as "causal modeling," cannot extract proof of causality from the covariance information being analyzed. Still, it's a good idea to systematically explore the limitations of structural equation modeling. So this class is basically about what this method cannot do. Besides, this sort of question is perfect for field exams.
Reading: Bollen (1989), ch. 3; Cliff (1983), "Some Cautions Concerning the Application of Causal Modeling Methods," Multivariate Behavioral Research, 18 (January), 115-126; Bullock, Harlow and Mulaik (1994), "Causation Issues in Structural Equation Modeling Research," Structural Equation Modeling: A Multidisciplinary Journal, 1 (August), 253-267.
Leading questions: (1) What definition of "causality" is consistent with statistical proof? (2) Under what conditions is it correct to interpret structural equation modeling results as evidence for causality?
Nov. 14 . . . Class 16: Equivalent Models
Talking about model comparisons raises the question, when are two models "the same?" Stelzl tried to answer this question with a set of rules.
Readings: Jöreskog and Sörbom (1989), pp. 221-4; Stelzl (1986), "Changing a Causal Hypothesis without Changing the Fit: Some Rules for Generating Equivalent Path Models," Multivariate Behavioral Research, 21 (July), 309-31 (tricky, since Stelzl uses lines between constructs to indicate the absence of a path between them!). A LISREL problem will be assigned.
Nov. 19 . . . Class 17: Analyzing non-MVN and ordinal data--PRELIS
Some researchers say this is a common situation that is too often ignored. Others say that this situation isn't ignored often enough.
Readings: Bollen (1989), pp. 433-46; Joreskog and Sorbom (1989), ch. 7; PRELIS instructions (handout). West, Finch and Curran (1995), "Structural Equation Models with Nonnormal Variables: Problems and Remedies," in Rick H. Hoyle (ed.), Structural Equation Modeling: Concepts, Issues and Applications (pp. 56-75)
Nov. 21 . . . Class 18: Respecifying the model for increased flexibility
Okay, now let's generalize the model, so that we can accommodate some special kinds of models. We'll do that by showing how the general model in LISREL is actually a special case of Submodel 3B--a submodel of the general model. We'll talk about specifying second-order factor models, and we may even discuss modeling interactions between latent variables.
Readings: Jöreskog and Sörbom (1989), ch. 6; Bollen (1989), pp. 395-400, 403-409; Rindskopf, David, and Todd Rose (1988), "Some Theory and Applications of Confirmatory Second-Order Factor Analysis," Multivariate Behavioral Research, 23 (January), 51-67; some additional notes may be assigned.
Nov. 26 . . . Class 19: Statistical Power
Statistical power considerations are just as important in SEM as they are with other techniques. However, the topic is much more complicated in this multivariate environment. Researchers should consider statistical power when making decisions about sample size and reaching conclusions about their research.
Readings: Kaplan (1995), "Statistical Power in Structural Equation Modeling," in Rick H. Hoyle (ed.), Structural Equation Modeling: Concepts, Issues and Applications (pp. 100-17). Also, possibly (I don't have the paper yet) MacCallum, Browne, and Sugawara (1996), "Power Analysis and Determination of Sample Size for Covariance Structure Modeling." Psychological Methods, 1, 130-149.