The University of North Carolina at Chapel Hill
School of Social Work
SOWO 916 Structural Equation Modeling
Spring Semester, 2013
INSTRUCTOR
Natasha K. Bowen, Ph.D.
Room 245E, Tate Turner Kuralt Building
CB #3550,
School of Social Work, Chapel Hill, NC 27599-3550
Phone: (919) 843-2434
Email: nbowen@email.unc.edu
CLASS MEETING TIMES & OFFICE HOURS
Class meets on Wednesdays 9:00-11:50 am in TTK Room 102
Office hours are Wednesdays 12:00 – 1:00 or by appointment
COURSE DESCRIPTION
This course was originally developed by Dr. Shenyang Guo. We will use much of his
syllabus, materials, and assignments throughout the semester.
Structural equation modeling (SEM) is a general statistical method that can be employed
to test theoretically derived models. It is “a class of methodologies that seeks to represent
hypotheses about the means, variances, and covariances of observed data in terms of a
smaller number of ‘structural’ parameters defined by a hypothesized underlying model”
(Kaplan, 2000). In this course, students will learn fundamental concepts and skills to
conduct SEM, and how to apply these techniques to social work research.
COURSE OBJECTIVES
At the completion of the course, students will be able to:
 Understand the fundamental hypothesis of SEM and its relationship to the
specification, identification, and estimation of a structural equation model;
 Run path analysis and test mediating hypotheses using SEM;
 Conduct confirmatory factor analysis to evaluate measurement validity;
 Conduct structural equations with latent variables and apply the method to
test/confirm a theoretically derived model;
 Understand statistical indices measuring goodness-of-fit of a model;
 Conduct multiple group comparisons with SEM to test moderating effects;
 Perform power analysis with SEM and know how to determine minimum sample
size needed;
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Understand basic concepts and skills to deal with interactions and quadratics in
latent variables, and categorical variables;
Understand the linkage between SEM and hierarchical linear models, and conduct
multilevel analysis and latent growth curve analysis with SEM;
Understand strategies for dealing with missing data.
PRE-REQUIREMENT
Students are assumed to be familiar with descriptive and inferential statistics. A solid
understanding of multiple regression analysis is a key. They should have statistical and
statistical software background at least equivalent to that provided by SOWO919 (applied
regression analysis and generalized linear models), SOCI209, PSYC282, EDUC284
(linear regression), or SOCI211 (categorical data analysis).
SOFTWARE PACKAGES
Students may choose to use SAS, SPSS, or Stata for data management and matrix
calculations. Class examples in these areas will be in Stata. The course will employ
Mplus for running SEM. Mplus is available through the university’s Virtual Computer
Lab. Students are expected to use the Lab’s help resources to learn how to establish
connections with the Lab.
TEXTBOOKS
Required:
Bowen, N. K., & Guo, S. (2011). Structural Equation Modeling. New York, NY: Oxford
University Press.
Recommended for students who will be conducting SEM’s in their futures:
Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: John
Wiley & Sons.
Byrne, B. M. (2012). Structural equation modeling with Mplus. New York: Routledge.
Hoyle, R. H. (Ed.). (2012). Handbook of structural equation modeling. New York:
Guilford Press.
Kline, R. (2011). Principles and Practice of Structural Equation Modeling, 3rd Ed., New
York: NY: Guilford Press.
ASSIGNMENTS
2 peer evaluations
5 IRATS
5 TRATS
Team Application Activities
7 Homeworks
GRADE PERCENTAGE
10%
15%
20%
20%
35%
TOTAL
100%
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GRADING SYSTEM
The standard School of Social Work interpretation of grades and numerical scores will be
used.
H = 94-100
P = 80-93
L = 70-79
F = 69 and below
POLICY ON CLASS ATTENDANCE
Class attendance is critical for team performance and individual learning. You are
expected to attend all scheduled sessions. Each class session will cover a great deal of
material, and you will fall behind in the course when you miss even one class. In
addition, your team will be disadvantaged by your absences. It is your responsibility to
inform the instructor in advance about missing a class session. Starting after the second
absence, your course grade will be reduced by 10% for each session missed. This
reduction will occur after the calculation of your final grade and will be in addition to the
effects absences may have on your peer evaluations. If you miss a class, you are
responsible for obtaining all notes, announcements, handouts, and assignments from the
missed class from your classmates. If you miss three classes, you will be expected to
meet with the instructor and Associate Dean of Student Services to discuss if further
participation in the course is possible. A grade of incomplete will only be given under
extenuating circumstances and in accordance with University policy.
POLICY ON INCOMPLETE AND LATE ASSIGNMENTS
Assignments are to be turned in to the instructor at the beginning of class on the due date
noted in the course outline if the class meets on a due date. If assignments are sent by
email, do not assume they have been received until confirmation is received. Extensions
may be granted by the professor given advance notice of at least 24 hours and
extenuating circumstances. Unannounced late assignments will automatically be reduced
10%. An additional 10% grade reduction on the assignment will occur for each day late
(including weekend days). A grade of incomplete will only be given under extenuating
circumstances and in accordance with University policy.
POLICY ON ACADEMIC DISHONESTY
In-class activities are designed to create a collaborative learning environment. However,
graded assignments are to be completed totally independently. Once an assignment has
been handed out, it is assumed that students will not discuss any aspect of the assignment
together—not even general principles or topics related to the assignment. Such exploring
or sharing of knowledge that is even peripherally related to class assignments gives an
unfair advantage to students who have peers from the same department or school enrolled
in the course. Violations constitute violations of the honor code and will be treated as
such.
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Please include the honor code statement along with your signature on all assignments:
“I have neither given nor received unauthorized aid on this assignment.”
This statement indicates to the instructor that you did not consult with students or other
human sources on any aspect of the assignment. It also represents your pledge that you
have not made use of information or materials related to graded assignments from last
year’s course. For assignments that are open book and take home (such as homeworks),
consulting non-human sources (text and online sources) is encouraged. For example, you
may read existing SEMNET postings, articles and Powerpoints about topics that are
posted online, and book chapters, but you may not post a question related to an
assignment to a discussion board. All questions about assignments and these policies
should be referred to the instructor.
Please refer to the APA Style Guide (6th edition), the SSW Manual, and the SSW Writing
Guide for information on attribution of quotes, plagiarism and appropriate use of
assistance in preparing assignments.
If reason exists to believe that academic dishonesty has occurred, a referral will be made
to the Office of the Student Attorney General for investigation and further action as
required.
POLICY ON ACCOMMODATIONS FOR STUDENTS WITH DISABILITIES
Students with disabilities that affect their participation in the course and who wish to
have special accommodations should contact the University’s Disabilities Services and
provide documentation of their disability. Disabilities Services will notify the instructor
that the student has a documented disability and may require accommodations. Students
should discuss the specific accommodations they require (e.g. changes in instructional
format, examination format) directly with the instructor immediately after the first class
session and before the second class session. Retroactive accommodations will not be
implemented. The instructor is happy to make any necessary accommodations to ensure
optimal learning for every student.
POLICIES ON THE USE OF ELECTRONIC DEVICES
IN THE CLASSROOM
We will discuss the use of laptops for in-class activities on the first day. The use of
electronic devices for non-class related activities (e.g. checking messages, playing
games) is prohibited. If any such uses occur during class time, laptops will not be allowed
for any students for the remainder of the course.
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DATES AND DESCRIPTIONS OF ASSESSMENTS AND HOMEWORK ASSIGNMENTS
DATE
1/9
1/23
1/30
2/6
2/13
2/20
2/27
3//6
3/20
3/27
4/3
4/10
4/17
4/23
ASSIGNMENT
DESCRIPTION
ASSESSMENT 1
HOMEWORK 1 DUE
HOMEWORK 2 DUE
ASSESSMENT 2
HOMEWORK 3 DUE
NO HW OR RAT!
ASSESSMENT 3
HOMEWORK 4 DUE
ASSESSMENT 4
HOMEWORK 5 DUE
HOMEWORK 6 DUE
ASSESSMENT 5
HOMEWORK 7 DUE
Matrices, Intro to SEM
Matrix algebra, basic statistics
Path analysis with traditional regression
Confirmatory factor analysis
Running an Mplus CFA
General structural models
Running an Mplus general structural model
SEM with ordinal and non-normal data
Running Mplus with WLSMV
Comparing analyses with Mplus’ clustered data options
Latent growth modeling
Running a Latent growth model in Mplus
Homework assignments are due at the beginning of class and must include the student
honor pledge (I have neither given nor received unauthorized assistance on this
assignment) to be accepted.
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OUTLINE OF COURSE TOPICS AND READINGS
1/9/13: Introduction to SEM and Underlying Statistics
(class 1)
1. Intro to TBL
2. Intro to SEM
Three types of SEMs
Basic statistical concepts—IRAT, TRAT
Path diagrams—Team Activity
5. Underlying hypothesis in SEM
1/16/13: No class—Read and study for next week
1/23/13: Matrices and Matrix Algebra
(class 2)
1. Many kinds of matrices
2. Manipulation of matrices
3. SEM specification—Path Diagrams and Matrices
Required readings and resources (recommended order, B & G, powerpoint, Bollen)
Bollen (1989), Appendix A: Matrix Algebra Review (focus on types of matrices,
major features of matrices, special matrices, and simple manipulations)
Bowen & Guo Chapers 1 & 2, pp. 3-51 (you may pay less attention to the parts
about equations)
Matrices Powerpoint
Recommended resources: Matrix operations review by Ender; Multivariate matrices; and
matrix operations in Stata, SPSS, SAS by Ender (Ender’s pdf file on matrix
algebra summarizes important matrix operations)
RAT1
Homework 1 assigned
1/30/13: Path Analysis I
(class 3)
1. Specification—Path diagrams, matrices, equations
2. Mediation
3. Identification
4. The concept of model fit
Required readings:
Bowen & Guo, Return to chapter 2 and read the sections about equations
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Kline, R. (2005). Principles and practice of structural equation modeling, 2nd ed.
New York, NY: Guilford Press. Chapter 5, pp. 93-122. (note: posted
chapter goes beyond p. 122; you only need to print to p. 122)
Homework 1 due at the beginning of class
Homework 2 assigned
2/6/13: Path Analysis II
(class 4)
1. Path analysis estimation in Mplus
2. More on the evaluation of fit (χ2)
3. Evaluation of parameters
4. Direct, indirect and total effects
Required readings: (recommended order—alphabetical)
Bowen & Guo, pp. 141 and 144 in Chapter 6 (on χ2)
Kline, R. (2005). Principles and practice of structural equation modeling, 2nd ed.
New York, NY: Guilford Press. Chapter 6, pp. 123-164.
Wu, Hui-ching (2011). The protective effects of resilience and hope on quality of
life of the families coping with the criminal traumatisation of its [sic]
members. Journal of Clinical Nursing, 20, 1906-1915. Available online at:
http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2702.2010.03664.x/pdf
Homework 2 due at the beginning of class
2/13/13: SEM with latent variables: Confirmatory Factor Analysis
(class 5)
1. Latent variables
2. Theory
3. Specification—path diagram, matrices, equations
4. Identification
5. More on model fit
Required readings (recommendation: read B&G, then Bollen):
Bollen, K. A. (2000). Modeling strategies: In search of the Holy Grail. Structural
Equation Modeling 7, 74-81.
Bowen & Guo, Chapter 4, pp. 73-108; and pp. 141-144 on χ2 in Chapter 6.
CFA Powerpoint
An optional (user-friendly) reading:
Iacobucci, D. (2009). Everything you always wanted to know about SEM but
were afraid to ask. Journal of Consumer Psychology, 19, 673-680.
RAT2
Homework 3 assigned
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2/20/13: Confirmatory Factor Analysis: A closer look
(class 6)
1. Alternative models
2. Second-order CFA models
3. Correlated measurement errors
4. Improving and comparing models--Intro
Required readings:
Bentler P. M. & Mooijaart, A. (1989). Choice of structural model via parsimony:
A rationale based on precision. Psychological Bulletin, 106, 315-317.
Bowen & Guo, Chapter 6, pp. 135-166 (some parts are review)
Gerbing, D. W. & Anderson, J. C. (1984). On the meaning of within-factor
correlated measurement errors. Journal of Consumer Research, II, 572-580.
Homework 3 due at the beginning of class
Midterm course feedback
2/27/13: Confirmatory Factor Analysis in Scale Development
(class 7)
1. Theory
2. Validity
3. Reliability
4. MIMIC models
5. Method effects and Multi-method multi-trait models
Required readings:
Eid, M., Nussbeck, F. W., Geiser, C., Gollwitzer, M., Cole, D. A., & Lischetzke, T.
(2008). Structural equation modeling of multitrait-multimethod data: Different
models for different types of methods. Psychological Methods, 13, 230-253.
Gregory, Jr., V. L. (2012). Gregory Research Beliefs Scale: Discriminant construct,
concurrent criterion, and known-groups validity. Journal of Evidence-Based
Social Work, 9, 465-480.
Pohl, S., & Steyer, R. (2012). Modeling traits and method effects as latent variables. In S.
Salzborn, Davidov, E., & Reinecke, J. (eds.). Methods, theories, and empirical
applications in the social sciences. Wiesbaden, Germany: Springer.
Reliability article TBA
Midterm peer evaluations
3/6/13: General SEM: Structural and measurement models combined
(class 8)
1. Theory
2. Specification-- path diagram, matrices, equations
3. Identification
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4. Estimation
5. Improving models
Required readings:
Anderson, J. C. and D. W. Gerbing (1988). Structural equation modeling in
practice A review and recommended two-step approach. Psychological
Bulletin 103, 411-423.
Bowen & Guo, chapter 5, pp. 109-134 and review chapter 6, pp. 157-166.
Ferron, J. M. and M. R. Hess (2007). Estimation in SEM: A concrete example.
Journal of Educational and Behavioral Statistics, 32: 110-120.
Rothbard, N. P. (2001). Enriching or depleting? The dynamics of engagement in
work and family roles. Administrative Science Quarterly, 46, 655-684.
RAT3
Homework 4 assigned
3/13/12: HAVE A GOOD SPRING BREAK!
3/20/12: Multiple Group Modeling
(class 9)
1. Path analysis
2. CFA
3. General structural models
Required readings:
Bowen & Guo, review Chapter 6, 149-157 and Chapter 7, pp. 180-186
Dimitrov, D. M. (2010). Testing for factorial invariance in the context of
construct validation. Measurement and Evaluation in Counseling and
Development, 43, 121-149.
Simons, R. L., Johnson, C., Beaman, J., Conger, R. D., and Whitbeck, L. B.
(1996). Parents and peer group as mediators of the effect of community
structure on adolescent problem behavior. American Journal of community
Psychology, 24, 145-171.
Werner, C. & Schermelleh-Engel. (2010). Deciding between competing models:
Chi-square difference tests. Available at:
http://user.uni-frankfurt.de/~cswerner/sem/chisquare_diff_en.pdf
Recommended:
Cheung, G. W. & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing
measurement invariance. Structural equation modeling, 9, 233-255.
Homework 4 due at the beginning of class
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3/27/12: Appropriate SEM Approaches for Social Science Data I
(class 10)
1. Robust Estimators for Non-Normal Measures
2. What to do With Ordinal Data
3. A note on multiple group analysis with WLSMV
Required readings:
Bowen & Guo, pp. 57-65 in Chapter 2
Flora, D. B., & Curran, P. J. (2004). An empirical evaluation of alternative
methods of estimation for confirmatory factor analysis with ordinal data.
Psychological Methods, 9(4), 466-491.
Sass, D. A. (2011). Testing measurement invariance and comparing latent factor
means within a confirmatory factor analysis framework. Journal of
Psychoeducational Assessment, 29, 347-363.
Wegmann, K. M., Thompson, A. M., & Bowen, N. K. (2010). A confirmatory
factor analysis of home environment and home social behavior data from
the ESSP for Families. Social Work Research, 35, 65-128.
RAT4
Homework 5 assigned
4/3/12: Appropriate SEM Approaches for Social Science Data II
(class 11)
1. Missing Data
2. Clustered Data
3. Power
Required readings:
Bowen & Guo, Chapter 3, pp. 52-72
Bowen & Guo Chapter 7, sections on power analysis and the problem of
underidentification, pp. 167-179
MacCallum, R.C., Browne, M.W., & Sugawara, H.M. (1996). Power analysis and
determination of sample size for covariance structure modeling,
Psychological Methods 1, 130-149.
Enders, C. K., & Bandalos, D. L. (2001). The relative performance of full
information maximum likelihood estimation for missing data in structural
equation models. Structural Equation Modeling, 8, 430-457.
Homework 5 due at the beginning of class
Homework 6 assigned
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4/10/13: Longitudinal Analyses in SEM--ARCL
(class 12)
1. Autoregressive, cross-lagged models
2. Specification
3. Identification
Required readings:
Cole, D. A. & Maxwell, S. E. (2003). Testing meditational models with
longitudinal data: Questions and tips in the use of structural equation
modeling. Journal of Abnormal Psychology, 112, 558-577.
Homework 6 due at the beginning of class
4/17/13: Longitudinal Analyses in SEM--Latent growth models
(class 13)
Required readings:
Curran, P. J., & Willoughby, M. T. (2003). Implications of latent trajectory
models for the study of developmental psychopathology. Development
and Psychopathology, 15. 581-612.
Latent growth modeling Powerpoint
RAT5
Homework 7 assigned
4/23/13: Follow-up, Catch-up, Wrap-up
Homework 7 due at the beginning of class
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