The University of North Carolina at Chapel Hill
School of Social Work
SOWO 719 Structural Equation Modeling
Fall Semester, 2009
INSTRUCTOR
Natasha K. Bowen, Ph.D.
Room 402J
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 Fridays 9:00-11:50 am in TTK Rm 107
Office hours are Fridays 12:00 – 1:00 or by appointment
COURSE DESCRIPTION
This course was developed and is usually taught by Dr. Shenyang Guo. We will make
heavy use 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 know 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;
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 dealing with missing data.
*We will examine these concepts only if time allows.
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 as the primary statistical software
package for data management and non-SEM statistical analysis, though the classroom
lectures and materials will be based on SPSS. The course will employ AMOS as the
main software package for running SEM. Advantages of Mplus will also be taught.
TEXTBOOKS
Required:
Kline R.B. (2005). Principles and practice of structural equation modeling, Second
edition. New York, NY: the Guilford Press.
Byrne, B.M. (2009). Structural Equation Modeling with AMOS: Basic Concepts,
Applications, and Programming. Mahwah, NJ: Lawrence Erlbaum Associates.
Recommended:
Bollen, K.A. (1989). Structural equations with latent variables. New York, NY: John
Wiley & Sons. (recommended but not required)
Kaplan, D. (2008). Structural Equation Modeling: Foundations and Extensions.
Thousands Oaks, CA: Sage Publications. (recommended but not required)
Long, J. Scott. (1983). Confirmatory factor analysis: A preface to LISREL. Newbury
Park, NY: Sage Publications.
2
READINGS ABOUT APPLICATIONS OF SEM TO SOCIAL WORK RESEARCH
A reading list of 139 articles, compiled by Shenyang Guo and Chung-Kwon Lee, will be
made available to students. These articles are applications of SEM to social work
research. We compiled the list by reviewing all articles in eight social-work or socialwork-related journals published from January 1, 1999 to December 31, 2004. These
articles will be used in classroom lectures as social work examples. They will also serve
as a useful literature base for students to learn various applications of SEM to social work
problems.
ASSIGNMENTS
Assignment 1
Assignment 2
Assignment 3
Assignment 4
Attendance and Preparation
Midterm Exam (take home)
Final Exam (take home)
GRADE PERCENTAGE
10%
10%
10%
10%
10%
25%
25%
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 an important element of class evaluation, and 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. It is the student’s
responsibility to inform the instructor in advance for missing a class session. Starting
after the second absence, your course grade will be reduced by 10% for each session
missed. This reduction may make it necessary for the student to drop the course to avoid
an inadequate grade. Students who miss a class are responsible for obtaining all notes,
announcements, handouts, and assignments from the missed class from their peers. 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 class does not meet on a
due date, assignments are due at 5:00 pm on the due date. If assignments are sent by
email, do not assume they have been received until confirmation is received. Extensions
3
may be granted by the professor given advance notice of at least 24 hours. Late
assignments will automatically be reduced 10 percent. An additional 10 percent grade
reduction 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
Students are absolutely expected to follow the UNC Honor Code. All graded
assignments are to be completed independently. 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. Assignments are open book and take home; 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 email a question related to an assignment to a
discussion board. All questions about assignments 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
Students may discuss with the instructor the possibility of using laptops during class on
the first day of class. Regardless of the decision made during this discussion, the use of
electronic devices for non-class related activities (e.g. checking email, playing games) is
4
prohibited. If any such uses occur during class time, laptops will not be allowed for the
remainder of the course.
DESCRIPTION OF THE ASSIGNMENTS
Assignment 1: Matrix algebra, basic statistics, and expectations. Due 9/18/09.
Assignment 2: Running AMOS to solve problems of path analysis and regression
analysis; and solving problems related to the decomposition of direct and
indirect effects. Due 10/2/09.
Midterm exam: Replicating a CFA study and testing an alternative factor model. Due
10/30/09.
Assignment 3: Evaluating, modifying, and comparing general SEM models. Due 11/6/09.
Assignment 4: Testing group differences. Appropriate strategies for problematic data.
Due 11/20/09.
Final exam:
Apply best practices in specification, estimation, evaluation of fit, and
model modifications. Due 12/11/09
5
OUTLINE OF COURSE TOPICS AND READINGS
8/28/09: Introduction to SEM and course overview
(class 1)
Required readings:
Kline Chapter 1, Byrne Chapter 1
(~30 pages)
9/04/09: Preliminaries (Part I): Basic matrix algebra
(class 2)
1. Matrix operations
2. Properties of matrix operations
3. Applications of matrix algebra to statistical analysis
4. The eight basic matrices of SEM
Required readings:
Bollen (1989), Appendix A
(~47 pages) Ask for guidance.
Kline Chapter 1, Byrne Chapter 1
Optional reading:
Guo & Bowen (in preparation), Chapters 1 and 2
9/11/09: Preliminaries (Part II): Covariance algebra, correlation, and regression
(class 3)
1. Variance, Covariance
2. Expectations
3. Standardization, covariance, and correlation
4. Regression, partial correlation, multiple correlation
5. Statistical assumptions of regression and diagnostics
6. Centered variables
Required readings:
Kline Chapters 2 & 3, Byrne pp. 102-106
(~50 pages)
Hays, W. L. (1981) “The algebra of expectations,” in Statistics for Psychologists, 3rd
Edition (pp. 667-671), New York: Holt, Rinehart and Winston. (Ask for guidance)
(Assignment 1 available on BB, due 9/18/09. Work independently.)
9/18/09: Path analysis & running AMOS
(class 4)
1. Path analysis
2. Total, direct, and indirect effects
3. Overview of running AMOS
Required readings:
Kline Chapters 5 & 6, and pp. 66-69. Byrne Chapter 2
(~100 pages) Ask for guidance
AMOS lab in Room 227
(Assignment 1 due at beginning of class)
6
9/25/09: A second pass at model specification, identification, and estimation in SEM
with latent variables, plus handling missing data
(class 5)
1. Steps and best practices in running SEM
2. The fundamental hypothesis
3. Missing data
Required readings:
Kline Chapter 4, Byrne Chapter 13
(~83 pages)
Hoyle, R. H. (1995). The structural equation modeling approach: Basic concepts
and fundamental issues. In R. H. Hoyle (Ed.), Structural equation
modeling: Concepts, issues, and applications (pp. 1-15). Thousand Oaks,
CA: Sage Publications.
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.
(Ask for guidance)
Optional readings:
Reread Kline Chapter 1, Byrne Chapter 1, Guo & Bowen Chapters 1 and 2
Joreskog, K. G. (1993). Testing structural equation models. In K. A. Bollen & J.
S. Long (Eds.). Testing Structural Equation Models. (pp. 294-316).
Newbury Park, CA: Sage Publications.
(Assignment 2 available on BB, due 10/2/09. Work independently.)
10/2/09: Confirmatory factor analysis (Part I)
(class 6)
1. Applications and best practices in CFA
2. Model specification
3. Identification
4. Equations and matrices
5. Three types of measurement models: parallel, Tau-equivalent, congeneric
6. Validity
Required readings:
Kline Chapter 7, Byrne Chapter 3 (especially up to p. 73) and Chapter 4
(~90 pages)
Optional reading:
Guo & Bowen (in preparation), chapter 4
Bride, B. E., Robinson, M. M., Yegidis, B., & Figley, C. R. (2004). Development
and Validation of the Secondary Traumatic Stress Scale. Research on
Social Work Practice, 14, 27-35.
AMOS lab in Room 227
(Assignment 2 due at beginning of class)
7
10/09/09: Confirmatory factor analysis (Part II)
(class 7)
1. Evaluation and modification of models
2. Second-order CFA models
3. Correlated measurement errors
4. Comparison of models (testing differences—1)
Required readings:
Byrne Chapter 5, up to p. 143
(~33 pages)
Gerbing, D. W. & Anderson, J. C. (1984). On the meaning of within-factor
correlated measurement errors. Journal of Consumer Research, II, 572-580.
Yap, J. C., et al. (2008). Validation of the Chinese pain catastrophizing scale
(HK-PCS) in patients with chronic pain. Pain Medicine, 9, 186-195.
Optional reading:
Guo, S. & Bowen, N. K. (in preparation). Chapter 6.
(Midterm exam distributed, due 10/30/09 at beginning of class. Work independently.)
10/16/09: General SEM (Part I): Structural and measurement models combined
(class 8)
1. Applications and best practices in general SEM
2. Model specification
3. Identification
4. Equations and matrices
Required readings:
Kline Chapter 8, Byrne Chapter 6
(~55 pages)
Optional reading:
Guo & Bowen, chapter 5
AMOS lab in Room 227
10/23/09: No Class. Happy Fall Break!
10/30/09: General SEM (Part II): Other models
(class 9)
1. Nonrecursive models
2. Mediation models
3. Alternative models (testing differences--2)
4. More on the evaluation and modification of models
Required readings:
Kline Chapter 9
(~49 pages)
Benda, B. B., & Corwyn, R. F. (2000). A theoretical model of religiosity and drug
use with reciprocal relationships: A test using structural equation
modeling. Journal of Social Service Research, 26, 43-67.
Optional reading:
Reread Byrne, pp. 73-95
8
Guo & Bowen, chapter 6
(Midterm due at the beginning of class)
(Assignment 3 available on BB, due 11/6/08. Work independently.)
11/06/09: Multiple-group comparison
(class 10)
1. Measurement invariance
2. Test moderating effects with SEM
3. MIMIC models
Required readings:
Byrne Chapters 7 & 9, Kline Chapter 11
(~65 pages)
Readings used in class (supplied by instructor)
Harford, T. C., Wechsler, H., & Muthen, B. O. (2003). Alcohol-related aggression
and drinking at off-campus parties and bars: A national study of current
drinkers in college. Journal of Studies on Alcohol, 64, 704-711.
Agrawal, A., & Lynskey, M. T. (2007). Does gender contribute to heterogeneity
in criteria for cannabis abuse and dependence? Results from the national
epidemiological survey on alcohol and related conditions. Drug and
Alcohol Dependence, 88, 300–307.
Mora, P. A., Contrada, R. J., Berkowitz, A., Musumeci-Szabo, T., Wisnivesky, J.,
& Halm, E. A. (2009). Measurement invariance of the Mini Asthma
Quality of Life Questionnaire across African–American and Latino adult
asthma patients. Quality of Life Research, 18, 371–380.
Optional reading:
Guo & Bowen, chapter on multiple group analysis
Bentler (1992), Byrne (1989, 1994, 1994), Bowen (2002) Ask instructor.
(Assignment 3 due at beginning of class)
(Assignment 4 available on BB, due 11/20/09. Work independently.)
11/13/09: Strategies for ordinal, clustered, and non-normal data, and power analysis
(class 11)
1. Non-normality and strategies
2. Categorical and ordinal variables and strategies
3. Grouped data and strategies
Required readings:
Byrne pp. 143-160 and Chapter 12
(~59 pages)
West, Finch, & Curran, (1995). Structural equation models with nonnormal
variables, in R. Hoyle (Eds.) Structural Equation Modeling (pp.56-75).
Thousands Oaks, CA: Sage Publications, Inc.
Optional reading:
Guo & Bowen, TBA
9
11/20/09: Longitudinal analysis with SEM (I)
(class 12)
1. Autocorrelated, cross-lagged models
2. Latent growth curve modeling
Required readings:
Kline Chapter 10, Byrne Chapter 11
(~78 pages)
Johan Ormel, J., Rijsdijk, F. V., Sullivan, M., van Sonderen, E., & Kempen, G. I.
J. M. (2002). Temporal and reciprocal relationship between IADL/ADL
disability and depressive symptoms in late life. Journal of Gerontology,
57B, 338-347.
Recommended readings:
Willett, J.B., & Sayer, A.G. (1994). Using covariance structure analysis to detect
correlates and predictors of individual change over time, Psychological
Bulletin 116, 363-381.
Chou, C., Bentler, P.M., & Pentz, M.A. (1998). Comparisons of two statistical
approaches to study growth curves: the multilevel model and the latent
curve analysis, Structural Equation Modeling 5, 247-266.
Aish, A., & Joreskog, K.G. (1990). A panel model for political efficacy and
responsiveness: An application of LISREL 7 with weighted least squares,
Quality & Quantity 24, 405-426
Pandey, S., & Coulton, C. (1994). Unraveling neighborhood change using twowave panel analysis: A case study of Cleveland in the 1980s, Social Work
Research 18, 83-96.
Curran, P.J., & Willoughby, M.T. (2003). Implications of latent trajectory models
for the study of developmental psychopathology, Development and
Psychopathology 15, 581-612.
(Assignment 4 due at beginning of class.)
(Final exam distributed, due 12/11/09)
11/27/09: No Class. Happy Thanksgiving!
12/4/09 Power, MPlus, Course summary
(Class 13)
1. Power analysis
2. Why MPlus?
3. Parting words of wisdom
Required readings:
Kline Chapter 12
(~40 pages)
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.
(Ask for guidance)
Reading on Mplus, TBA
Optional readings (for future reference):
10
Boomsa, A. (2000). Reporting analyses of covariance structures, Structural
Equation Modeling 7, 461-483.
Hoyle, R. H., & Panter, A. T. (1995). Writing about structural equation models, In
R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues, and
applications (pp. 158-176). Thousand Oaks, CA: Sage Publications.
MacCallum, R.C., Browne, M.W., & Cai, L. (2006). Testing differences between
covariance structure models: Power analysis and null hypothesis.
Psychological Methods, 11, 19-35.
12/11/08: Final exam due by 5:00, at instructor’s office, mailbox, or by email. Seek
confirmation of receipt.
11