The University of North Carolina at Chapel Hill
School of Social Work
SOWO 916 Structural Equation Modeling
Spring Semester, 2015
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 101
Office hours are Wednesdays 12:00 – 1:00 or by appointment
This course was originally developed by Dr. Shenyang Guo.
COURSE DESCRIPTION
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
Final Exam
TOTAL
GRADE PERCENTAGE
10%
10%
15%
30%
14%
21%
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 TRATs and application activities are designed to create a collaborative learning
environment. However, IRATs, homeworks, and the final exam 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
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, TOPICS, AND DESCRIPTIONS OF ASSESSMENTS AND HOMEWORK ASSIGNMENTS
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DATE ASSIGNMENT
HW 1 assigned: OLS
1/7
regression, Mplus & virtual
computer lab
1/14 RAT 1
HW 1 due
HW 2 assigned: Direct/Ind
effects
1/21 HW 2 due
4
1/28
5
2/4
6
2/11
7
2/18
8
2/25
9
3/4
1
2
DESCRIPTION
Introduction to SEM and Team-based
Learning
Path analysis I: Specification, direct &
indirect effects
Path analysis II: Identification, fit,
parameter estimates; Intro to matrices
Matrices in SEM
RAT 2
HW 3 assigned: CFA on
your own
HW 3 due
HW 4 assigned: Justifiable
modifications
HW 4 due
Confirmatory factor analysis I: Theory,
specification, identification
General structural models: Theory,
specification, identification, alternative
models
Options for special data: Non-normal,
ordinal, clustered data and data with
missing values
11 3/25
RAT 3
HW 5 assigned: General
SEM on your own
HW 5 due
HW 6 assigned: Special
analyses on your own
Task: identify 2 articles in
your area of interest, bring to
class next week
HW 6 due
Bring two SEM articles
HW 7 assigned: Article
critique
RAT 4
12 4/1
HW 7 due
13 4/8
14 4/15
15 4/22
RAT 5
Longitudinal Models I: Repeated
Measures
Longitudinal Models II: Growth Curves
Advanced Readings in SEM
10 3/18
CFA II: Alternative models,
modifications, correlated errors
CFA III: CFA in Scale development
Critiquing SEM studies
Power analysis
Multiple Group Analysis
Final exam
Reminder: 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
1/7/15: Introduction to SEM and Team-based Learning
(class 1)
1. Intro to TBL
2. Intro to SEM
HW1 assigned
Also by next week, become versatile at gaining access to Mplus 7 at the UNC virtual lab,
and finding files on your computer while using the virtual lab. Mplus is now at the new
virtuallab.unc.edu address. Intra- and inter-team information sharing about using the
virtual lab is encouraged. The virtual lab website also has helpful information.
1/14/15: Path Analysis I: Specification, Direct and Indirect Effects
(class 2)
1. Specification—Path diagrams, equations, Mplus syntax
2. Direct and indirect effects
3. Mplus: running path models
4. Examining path coefficients
RAT1
HW1 due
Required readings for today:
Bowen & Guo, chapter 1, pp. 1-15; part of chapter 2, pp.17-34; pp. 202-203
Kline, R. (2005). Principles and practice of structural equation modeling, 2nd ed.
New York, NY: Guilford Press. pp. 93-105 and 123-131, 162.
Optional readings to strengthen understanding (read now or any time during semester):
Bagozzi, R. P., & Yi, Y. (1988). On the evaluation of structural equation models.
Journal of the Academy of Marketing Science, 16(1), 74-94.
Homework 2 assigned
1/21/15: Path Analysis II: Identification, Fit, Parameter Estimates, Intro to Matrices
(class 3)
1. Identification
2. Mplus: running path models
4. A first look at the evaluation of fit
5. An intro to the many matrices of SEM
HW2 due
Required readings: (recommended order—alphabetical)
Bowen & Guo, pp. 49 – 51 in chapter 2; pp. 141-149 in chapter 6
Kline, R. (2005). Principles and practice of structural equation modeling, 2nd ed.
New York, NY: Guilford Press. pp. 105-120, 131-150.
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1/28/15: Matrices in SEM
(class 4)
1. Input matrix generation from raw data
2. Input, implied, and residual matrices
3. Specification of path models with matrices
4. Matrix operations with analysis matrices
Required readings (recommended order, B & G, Bollen):
Bollen (1989), Appendix A: Matrix Algebra Review (also see posted guide to the
Appendix)
Bowen & Guo Chaper 2, pp. 34-49
Additional resources are posted: Matrix operations review by Ender; Multivariate
matrices; and matrix operations in Stata by Ender (Ender’s pdf file on matrix
algebra summarizes important matrix operations) Let me know if you prefer
information on matrix operations in SPSS or SAS.
2/4/15: Confirmatory Factor Analysis I: Theory, Specification, Identification
(class 5)
1. Latent variables
2. Classical Test Theory
3. Specification—path diagram, equations, matrices, Mplus
4. Identification
5. More on model fit
RAT 2
Required readings (recommendation: read B&G, Byrne, 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.
Byrne, B. M. (2005). Factor analytic models: Viewing the structure of an
assessment instrument from three perspectives. Journal of Personality
Assessment, 85(1), 17-32.
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.
HW 3 assigned
2/11/15 Confirmatory Factor Analysis II: Alternative models, modifications,
correlated errors
(class 6)
1. Alternative models
2. Second-order CFA models
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3. Correlated measurement errors
4. Improving and comparing models--Intro
HW 3 due
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.
Werner, C. & Schermelleh-Engel. (2010). Deciding between competing
models:Chi-square difference tests. (Posted at website.) Retrieved in 2013
at: http://user.uni-frankfurt.de/~cswerner/sem/chisquare_diff_en.pdf
HW 4 assigned
2/18/15: Confirmatory Factor Analysis III: CFA in Scale Development
(class 7)
1. Theory
2. Validity
3. Reliability
4. Method effects and Multi-method multi-trait models
HW 4 due
Required readings:
Bowen & Guo, review pp. 73-81 in chapter 4
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.
Midterm peer evaluations
Midterm course feedback
2/25/15: General SEM: Theory, Specification, Identification, Estimation, Model
Improvement
(class 8)
1. Theory
2. Specification-- path diagram, matrices, equations
3. Identification
4. Estimation
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5. Improving models
RAT 3
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 , pp. 157-166 in chapter 6
Rothbard, N. P. (2001). Enriching or depleting? The dynamics of engagement in
work and family roles. Administrative Science Quarterly, 46, 655-684.
Optional user friendly article:
Iacobucci, D. (2010). Structural equations modeling: Fit indices, sample size, and
advanced topics. Journal of Consumer Psychology, 20(1), 90-98.
Homework 5 assigned
3/4/15: Options for Special Data: Non-normal, Ordinal, Clustered Data, and Data
with Missing Values
(class 9)
HW 5 due
Required Readings:
Allison, P. D. (2003). Missing data techniques for structural equation modeling.
Journal of Abnormal Psychology, 112, 545-557.
Bowen & Guo, Chapter 3, pp. 52-72
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.
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.
Optional article and good reference on missing value analysis:
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.
HW 6 assigned
Also for 3/18, find two SEM articles in your area of interest. Bring them to me for review
as possible articles for your article critique (HW 6)
3/11/15: HAVE A GOOD SPRING BREAK!
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3/18/15: Critiquing SEM studies, Power Analysis
(class 10)
1. Critiquing SEM studies
2. Power analysis for SEM studies
HW 6 due
Bring two SEM articles to class for my review
Required readings:
Boomsma, A. (2000). Reporting analyses of covariance structures. Structural
Equation Modeling: A Multidisciplinary Journal, 7(3), 461-483.
Bowen & Guo, review Chapter 3, pp. 52-72
Bowen & Guo Chapter 7, sections on power analysis and the problem of
underidentification, pp. 167-179
Lee, T, Cai, L., MacCallum, R. C. (2012). Power analysis for tests of structural
equation models. In R. H. Hoyle (Ed.). Handbook of structural equation
modeling. (pp. 181-194). New York: Guilford Press.
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.
HW 7 assigned
3/25/15: Multiple Group Modeling
(class 11)
1. Path analysis
2. CFA
3. General structural models
4. Ordinal data
RAT 4
Required readings:
Bowen & Guo, review Chapter 6, 149-157 and Chapter 7, pp. 180-186
Campbell, H. L., Barry, C. L., Joe, J. N., and Finney, S. J. (2008). Configural,
metric, and scalar invariance of the modified achievement goal questionnaire
across African American and White university students. Educational and
Psychological Measurement, 68, 988-1007.
Dimitrov, D. M. (2010). Testing for factorial invariance in the context of
construct validation. Measurement and Evaluation in Counseling and
Development, 43, 121-149.
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.
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
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structure on adolescent problem behavior. American Journal of
Community Psychology, 24, 145-171.
Recommended:
Cheung, G. W. & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing
measurement invariance. Structural Equation Modeling, 9, 233-255.
4/1/15: Longitudinal Analyses in SEM I—Repeated Measures Models
(class 12)
1. Autoregressive, cross-lagged models
2. Specification, correlated errors
3. Identification
HW 7 due
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.
Find and read a recent SEM mediation study in your area of interest
Be prepared to discuss its strengths and weaknesses
4/8/15: Longitudinal Analyses in SEM II--Latent Growth Models
(class 13)
RAT 5
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.
Find and read a recent SEM growth model study in your area of interest
Be prepared to discuss its strengths and weaknesses
4/15/15: Advanced Readings
(class 14)
Ferron, J. M. and M. R. Hess (2007). Estimation in SEM: A concrete example.
Journal of Educational and Behavioral Statistics, 32: 110-120
Raykov, T., Marcoulides, G. A., & Li, C. (2012). Measurement invariance for
latent constructs in multiple populations: A critical view and refocus.
Educational and Psychological Measurement, 72, 954-972.
Tomarken, A. J., & Waller, N. G. (2003). Potential problems with “well fitting”
models. Journal of Abnormal Psychology, 112(4), 578-598.
Others TBA
4/22/15: Final Exam, in-class
(class 15)
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