Course Syllabus
Title of Course [Latent Variable Models and Structure Equations]
Prefix and Number [ED_PSYCH 582]
Semester and Year [Fall 2026]
Number of Credit Hours [3]
Prerequisites [ED_RES 565 Quantitative Research]
Recommended Preparation [ED_PSYCH 569 Seminar in Quantitative Techniques in Education]
Course Details
Day and Time: Thursday, 4:10 PM – 7:00 PM
Meeting Location: Cleveland Hall 63
Instructor Contact Information
Instructor Name: Shenghai Dai
Instructor Contact Information:
- Office: Cleveland Hall 354
- Phone: (509) 335-0958
- Email: s.dai@wsu.edu
Instructor Office Hours: Thursdays: 2:00 – 4:00 PM or by appointment
TA Name: [tbd]
TA Contact Information: [office location, phone, email]: [tbd]
TA Office Hours: [tbd]
Course Description
Ed Psych 582 aims to introduce classical and novel methods in covariance structure analysis and latent variable modeling and their applications in broad educational contexts. Topics investigated over the course of the semester include structural equation models, latent regression models, multiple-group models, latent growth models, latent mixture models, multilevel path and structure equation models, and models with categorical variables.
The course will primarily consist of lectures and practical exercises based on the assigned readings and examples. Each topic will be introduced with a lecture, followed by a prompted real data example and reflection on the topic discussed. During the semester, you are expected to complete readings prior to class, engage in practice and discussion during class periods, and complete several assignments. You are expected to select a topic of your interest within your area of research and provide in-depth analysis in both written and oral forms (see more detail below under Research Project). You are expected to actively participate and build on the knowledge previously acquired and to gain technical foundations necessary to be consumers and contributors to applied and methodological research using structure equations and/or latent variable models.
Course Materials
Books
- Bollen, K. A. (1989). Structural equations with latent variables. John Wiley & Sons. [Cost: New for $136 and used for about $26 on Amazon.]
Other Materials:
Other/Alternate Textbooks (Only Optional)
- Bollen, K. & Curran, P. (2006). Latent curve models: A structural equation perspective. Hoboken, NJ: Wiley.
- Hoyle, R. H. (2012). Latent variables in structural equation modeling. London: The Guilford Press.
- Kaplan, D. (2009). Structural equation modeling: Foundations and extensions (2nd ed.). Los Angeles: Sage.
- Long, S. Covariance structure models: An introduction to LISREL #34. Beverly Hills, CA: Sage Publications, Inc.
- Loehlin, J. C. (2004). Latent variable models: An introduction to factor, path, and structural equation analysis. Psychology Press.
- Marcoulides, G. A., & Moustaki, I. (Eds.). (2014). Latent variable and latent structure models. Psychology Press.
Recommended Other Book
- American Psychological Association (2019). Publication manual of the American Psychological Association (7th ed.). Washington, D. C.: Author.
Suggested Readings (for assigned readings, see Tentative Class Schedule)
- Basic Concepts & Structure Equations
- Muthén, B. O. (2002). Beyond SEM: General latent variable modeling. Behaviormetrika, 29(1), 81-117.
- Bentler, P. (1983). Simultaneous equation systems as moment structure models. Journal of Econometrics, 22 (1-2), 13-42.
- Bentler, P. & Dudgeon, P. (1996). Covariance structure analysis: Statistical practice, theory, and directions. Annual Review of Psychology, 47, 563-592.
- Nachtigall, C., Kroehne, U., Funke, F., & Steyer, R. (2003). (Why) should we use SEM? Pros and cons of structural equation modeling. Methods of Psychological Research Online, 8 (2), 1-22.
- Tomarken, A. & Waller, N. (2005). Structural equation modeling: Strengths, limitations, and misconceptions. Annual Review of Clinical Psychology, 1, 31-65.
- Model Specification and Identification
- Bollen, K. & Davis, W. (2009). Two rules of identification for structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 16 (3), 523-536.
- Burke-Jarvis, C., MacKenzie, S. & Podsako_, P. (2012). The Negative Consequences of Measurement Model Misspecification: A Response to Aguirre-Urreta and Marakas. MIS Quarterly, 36(1), 139-146.
- Latent Variables and Measurement Error
- Bollen, K. (2002). Latent variables in psychology and the social sciences. Annual Review of Psychology 53, 605-634.
- Rhemtulla, M., van Bork, R., & Borsboom, D. (2020). Worse than measurement error: Consequences of inappropriate latent variable measurement models. Psychological methods, 25(1), 30.
- Schennach, S. M. (2016). Recent advances in the measurement error literature. Annual review of economics, 8(1), 341-377.
- Cohen, P., Cohen, J., Teresi, J., Marchi, M., & Velez, C. N. (1990). Problems in the measurement of latent variables in structural equations causal models. Applied Psychological Measurement, 14(2), 183-196.
- Gerbing, J. & Hunter, J. (1982). The metric of the latent variables in a LISREL-IV analysis. Educational & Psychological Measurement 42, 423-427.
- Continuous Measurement Models
- Edwards, J. R., & Bagozzi, R. P. (2000). On the nature and direction of the relationship between constructs and measures. Psychological Methods, 5, 155-174.
- Jarvis, C., MacKenzie, & Podsako, P. (2003). A critical review of construct indicators and measurement model misspecification in marketing and consumer research. Journal of Consumer Research, 30(2), 199-218.
- Categorical Measurement Models
- Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological methods, 17(3), 354.
- Finney, S. J., & DiStefano, C. (2006). Non-normal and categorical data in structural equation modeling. Structural equation modeling: A second course, 10(6), 269-314.
- Li, C. H. (2021). Statistical estimation of structural equation models with a mixture of continuous and categorical observed variables. Behavior research methods, 53(5), 2191-2213.
- Monroe, S., & Cai, L. (2015). Evaluating structural equation models for categorical outcomes: A new test statistic and a practical challenge of interpretation. Multivariate behavioral research, 50(6), 569-583.
- Muthén, B. (1983). Latent variable structural equation modeling with categorical data. Journal of Econometrics, 22(1-2), 43-65.
- Model Fit Assessment
- Bentler, P. & Bonett, D. (1980). Signi_cance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin, 88 (3), 588-606.
- Bryant, F. & Satorra, A. (2012). Principles and practice of scaled difference chi-square testing. Structural Equation Modeling, 19, 372-398.
- Fan, X., & Sivo, S. A. (2005). Sensitivity of fit indices to misspecified structural or measurement model components: Rationale of two-index strategy revisited. Structural Equation Modeling, 12, 343-367.
- Shi, D., DiStefano, C., Maydeu-Olivares, A., & Lee, T. (2022). Evaluating SEM model fit with small degrees of freedom. Multivariate behavioral research, 57(2-3), 179-207.
- Measurement Invariance & Multiple Group Models
- Byrne, B., Shavelson, R., & Muthén, B. (1989). Testing for the equivalence of factor covariance and mean structures: The issue of partial measurement invariance. Psychological Bulletin, 105 (3), 456-466.
- Kim, E. S., & Yoon, M. (2011). Testing measurement invariance: A comparison of multiple-group categorical CFA and IRT. Structural Equation Modeling, 18(2), 212-228.
- French, B. & Finch, W. H. (2006). Confirmatory factor analytic procedures for determining measurement invariance. Structural Equation Modeling, 13 (3), 378-402.
- Meade, A. W., & Lautenschlager, G. J. (2004). A comparison of item response theory and confirmatory factor analytic methodologies for establishing measurement equivalence and invariance. Organizational Research Methods, 7, 361-388.
- Multilevel Path and SEM
- Kaplan, D., & Elliott, P. R. (1997). A didactic example of multilevel structural equation modeling applicable to the study of organizations. Structural Equation Modeling, 4, 1-24.
- Kaplan, D., & Kreisman, M. B. (2000). On the validation of indicators of mathematics education using TIMSS: An application of multilevel covariance structure modeling. International Journal of Educational Policy, Research, and Practice, 1, 217-242.
- Latent Regressions
- Kvalheim, O. M., & Karstang, T. V. (1989). Interpretation of latent-variable regression models. Chemometrics and intelligent laboratory systems, 7(1-2), 39-51.
- Li, D., Oranje, A., & Jiang, Y. (2009). On the estimation of hierarchical latent regression models for large-scale assessments. Journal of Educational and Behavioral Statistics, 34(4), 433-463.
- Christensen, K. B., Bjorner, J. B., Kreiner, S., & Petersen, J. H. (2004). Latent regression in loglinear Rasch models. Communications in Statistics-Theory and Methods, 33(6), 1295-1313.
- Latent Growth Models
- McArdle, J. J., & Bell, R. Q. (2000). An introduction to latent growth models for developmental data analysis. Modeling longitudinal and multilevel data: Practical issues, applied approaches, and specific examples, 69-107.
- Hancock, G. R., Kuo, W. L., & Lawrence, F. R. (2001). An illustration of second-order latent growth models. Structural Equation Modeling, 8(3), 470-489.
- Shi, D., DiStefano, C., Zheng, X., Liu, R., & Jiang, Z. (2021). Fitting latent growth models with small sample sizes and non-normal missing data. International Journal of Behavioral Development, 45(2), 179-192.
- Latent Mixture Models
- Kim, M., Vermunt, J., Bakk, Z., Jaki, T., & Van Horn, M. L. (2016). Modeling predictors of latent classes in regression mixture models. Structural Equation Modeling: A Multidisciplinary Journal, 23(4), 601-614.
- Muthén, B. O. (2001). Latent variable mixture modeling. In New developments and techniques in structural equation modeling (pp. 21-54). Psychology Press.
- Hancock, G. R., & Samuelsen, K. M. (2007). Advances in latent variable mixture models. IAP.
- Reporting Results
- 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.
- Boomsma, A. (2000). Reporting analyses of covariance structures. Structural Equation Modeling, 7 (3), 461483.
- McDonald, R.P., Ho, M. (2002). Principles and practice in reporting structural equation analyses. Psychological Methods, 7, 64-82.
- Applications
- MacCallum, R. & Austin, J. (2000). Applications of structural equation modeling in psychological research. Annual review of psychology, 51 (1), 201-227.
- Marten, M. & Haase, R. (2006). Advanced applications of structural equation modeling in counseling psychology research. The Counseling Psychologist, 34, 878-911.
Software
Computer lab work is a component of the course. This will give the student the opportunity to apply what is discussed in class. The R software (https://cran.r-project.org) is used as the major tool for the class. Other software (Mplus, Jamovi) will also be introduced as time allows or need arises. All the software tools are free of cost. To get familiar with R modeling, the following resources can be useful.
- Finch, W. H., & French, B. F. (2015). Latent variable modeling with R. Routledge, NY: New York.
- Albano, T. (2018) Introduction to Educational and Psychological Measurement Using R. Creative Commons Attribution 4.0 International License. (Available online at https://cehs01.unl.edu/aalbano/intro-measurement-r)
- Fox, J. (2006). Teacher's corner: structural equation modeling with the sem package in R. Structural equation modeling, 13(3), 465-486.
- Kwahk, K. Y. (2019). Structural equation modeling using R: Analysis procedure and method. Knowledge Management Research, 20(1), 1-26.
Fees: [NA]
Course Format
The class will include a variety of activities: individual work, class discussions, lab practices, small group work and presentations. Please come to class prepared to discuss reading and other assignments.
|
Course Learning Outcomes (students will be able to:) |
Activities Supporting the Learning Outcomes | Assessment of the Learning Outcomes |
|---|---|---|
|
Articulate the similarities and differences between latent variable models and structure equation models, and conduct analyses using structure equations with observed variables. |
Weeks 1-3: basic concepts of latent models and structural equations with observed variables |
Lab practice; Homework #1 |
|
Investigate model specifications and evaluate if the model is identified. |
Week 4: model specification and identification |
Lab practice; Homework #1 |
|
Select appropriate estimation methods to conduct analysis using measurement models with variables of different nature and scales; evaluate the model data fit using appropriate methods and indices; and interpret the results clearly. |
Weeks 5-7: continuous and categorical measurement models; model estimations and fit assessment |
Lab practice; Homework #2 |
|
Articulate the procedures of using multiple group models to investigate measurement invariances and model generalizability across groups. |
Weeks 8-9: measurement invariance and multiple-group models |
Lab practice; Homework #3 |
|
Conduct analysis using multilevel path model and SEM, and interpret the results. |
Week 10: multilevel path model and SEM |
Lab practice; Homework #4 |
|
Apply latent regressions with data, and interpret the results. |
Week 11: latent regressions |
Lab practice; Homework #4 |
|
Conduct analysis using latent growth models and interpret the results. |
Week 12: latent growth models |
Lab practice; Homework #5 |
|
Conduct analysis using latent mixture models and SEM, and interpret the results. |
Week 13: latent mixture models |
Lab practice; Homework #5 |
|
Implement a specific method learned in class in your area of research, propose and accomplish a research project (proposal, presentation, and research paper). |
Weeks 1-16; (Week 15: Project work and consultation; Week 16: Project presentation) |
Project proposal; presentation; Research project. |
| Dates | Lesson Topic | Assignment | Assessment |
|---|---|---|---|
|
Week 1 |
Overview of the course; review of statistical concepts; basic concepts of latent variable models, structural equations, and covariance structures |
Bollen (1984, CH1-2); |
HW#1 |
| Week 2 [09-03] |
Structure equations with observed variables, path models, mediations and moderations |
Bollen (1984, CH4); |
|
| Week 3 [09-10] |
Latent variable models, measurement error, causal models |
Bollen (1984, CH3,5,6); |
|
| Week 4 [09-17] |
Model specification and identification |
Bollen & Davis (2009); |
|
| Week 5 [09-24] |
Continuous measurement models |
Bollen (1984, CH6); |
HW#2 |
| Week 6 [10-01] |
Categorical measurement models |
Rhemtulla et al. (2012); |
|
| Week 7 [10-08] |
Combine observed and latent variables; |
Bentler & Bonett (1980); |
HW#3 |
| Week 8 [10-15] |
Measurement invariance and multiple-group models |
Byrne et al. (1989); |
|
| Week 9 [10-22] |
Software and analysis practice |
NA |
|
| Week 10 [10-29] |
Multilevel path models and SEM |
Kaplan & Elliott (1997); |
HW#4 |
| Week 11 [11-05] |
Latent regressions |
Kvalheim & Karstang (1989); |
|
| Week 12 [11-12] |
Latent growth models |
McArdle & Bell (2000); |
HW#5 |
| Week 13 [11-19] |
Latent mixture models |
Kim et al. (2016); |
|
| Week 14 [12-03] |
Project work and consultation | NA | Research Project |
| Week 15 [12-10] |
Project Presentations | NA | Presentation |
Notes: HW = homework
- The instructor reserves the right to adjust the schedule as needed.
- Additional readings may be assigned.
Expectations for Student Effort
For each hour of lecture equivalent, students should expect to have a minimum of two hours of work outside of class. I expect all students to (a) attend class on time, (b) participate actively in class discussions, (c) read all assigned readings, and (d) turn in assignments on time. We will try to have lab time each class session to practice what we have discussed. If you are unable to attend class, please notify me in advance. You are responsible for the information missed during your absence. No late assignments are accepted for credit.
Grading
| Type of Assignment (tests, papers, etc) | Points | Percent of Overall Grade |
|---|---|---|
| Homework Assignment | 50 | 50% |
| Research Project Proposal | 10 | 10% |
| Research Project Presentation | 10 | 10% |
| Research Project Paper | 30 | 30% |
Grades will be based on (a) homework assignments (50%) and (b) research project (50%). You are encouraged to work together on the data analysis part of the assignment and assist each other with the course material. However, all the other parts of the assignments, including article critique, results write-up for the analysis, and responses to the questions, should be your own work. Academic honesty is expected. Late Policy: Assignments turned in after the due date will not be eligible for credit toward the final grade you earn. Late assignments will be worth 0 points.
The course grade a student earns is determined by the following combination of assessments of the objectives listed above. I also note that you should expect to spend a few hours on homework assignments and work throughout the semester on your project. A last-day effort on assignments is not a robust strategy for mastering the content.
Homework Assignments [50%]
There will be a total of five homework assignments throughout the course [10% each]. The assignments will consist of practices or problems in related topics discussed in class, but also may include other learning/practice experiences. The data for the assignments and further assignment information will be provided. No make-up assignments will be offered. Late assignments are not accepted for credit. Assignments are due at the beginning of class, with no exceptions.
Research Project & Presentation [50%]
The purpose of the project is to provide you with an opportunity to apply skills learned in this class by investigating a problem of your interest through simulated or real data analysis. The project involves conducting a latent variable and structural equation modeling based study on data that are of interest to you. The dataset can be obtained from one of your professors, colleagues, or one that you have collected. A methodological study (i.e., simulation study) of an aspect of methodology is also encouraged. If you have questions about a data source, please ask. I can also generate data for you but need sufficient time to do so (i.e., 3-4 weeks). Projects will be presented to the class at the end of the semester. The written report is due 11: 59 PM on the Friday of the final exam week.
There are three graded components of the project:
- Project proposal (10%)
The project proposal should focus mainly on the research question, a brief literature review, and the study design (1-3 pages);
- Project presentation (10%)
Each individual or group will present their project at the end of the semester. This will be in the conference presentation style. Each team will have 10-12 minutes to present the project and a chance to answer questions from their colleagues.
- Project paper (30%)
The project report must be typed (double-spaced) and follow APA format (7th edition). The APA style manual is available at the bookstore and in the reference section of the library. Font size should be no smaller than 10 or larger than 12 point. Page margins should be 1.0 inch. The paper should be written in a form suitable for publication or submission for a conference paper in your area with a limit of 800 -2000 words, excluding references, tables, and figures. The range of possible projects is very broad and each paper should include: a) title page ( title ≤ 15 words), b) abstract (≤ 250 words), c) introduction (theoretical rationale, literature review, purpose statement, & hypothesis), d) method and study design, e) analysis and results, f) discussion (implications, limitations, etc.), and g) references. Computer programs (e.g., R code) and sample output from the analysis must be provided with the paper. More details will be given in class. Please proofread your work carefully. Incorrect grammar, misspelled words, and not following APA format are unacceptable. Projects given to me after the due date will not be eligible for credit toward your final grade.
| Grade | Percent | Grade | Percent |
|---|---|---|---|
| A |
100.00-93.00% |
C |
76.99-73.00% |
| A- |
92.99-90.00% |
C- |
72.99-70.00% |
| B+ |
89.99-87.00% |
D+ |
69.99-67.00% |
| B |
86.99-83.00% |
D |
66.99-60.00% |
| B- |
82.99-80.00% |
F |
59.99% or below |
| C+ |
79.99-77.00% |
Note: I reserve the right to change the scale if in favor of the student and I round to the nearest whole number.
Attendance and Make-Up Policy
Students should make all reasonable efforts to attend all class meetings. However, in the event a student is unable to attend a class, it is the responsibility of the student to inform the instructor as soon as possible, explain the reason for the absence (and provide documentation, if appropriate), and makeup class work missed within a reasonable amount of time, if allowed. Missing class meetings may result in a reduction in the overall grade in the class.
Assigning Incompletes: University policy (Acad. Reg. #90) states that Incompletes may only be awarded if: "the student is unable to complete their work on time due to circumstances beyond their control".
Academic Integrity Statement
You are responsible for reading WSU's Academic Integrity Policy, which is based on Washington State law.
Academic integrity is the cornerstone of higher education. As such, all members of the university community share responsibility for maintaining and promoting the principles of integrity in all activities, including academic integrity and honest scholarship. Academic integrity will be strongly enforced in this course. Students who violate WSU’s Academic Integrity Policy (identified in Washington Administrative Code (WAC) 504-26-010(3) and -404) will result in action of failing the assignment and/or course depending on the nature of the offense in accord with the policy, will not have the option to withdraw from the course pending an appeal, and will be reported to the Office of Student Conduct.
Cheating includes, but is not limited to, plagiarism and unauthorized collaboration as defined in the Standards of Conduct for Students, WAC 504-26-010(3). You need to read and understand all of the definitions of cheating: http://app.leg.wa.gov/WAC/default.aspx?cite=504-26-010. If you have any questions about what is and is not allowed in this course, you should ask course instructors before proceeding.
If you wish to appeal a faculty member's decision relating to academic integrity, please use the form available at conduct.wsu.edu.”
Attention to this policy is particularly important in a course like ED_PSYCH 580, in which collaboration with other students is encouraged. Specifically, you can only make use of the following sources when working on your homework assignments and exams. Other sources such as asking or paying others to do the work or similar are not acceptable and will be treated as violations of the WSU academic code (WAC 504-26-010).
- Lecture and lab notes, course materials, or other public-available text-based sources. These materials should not be used by copying and pasting, and should be credited appropriately (e.g., cited).
- Discussion with peers in class. If you work with other students during the planning, execution, or interpretation of your data analyses – a process that I support – you should make sure that the other students’ contributions are recognized explicitly in your written account.
- Asking me for help.
If you cheat in your work in this class you will:
- Fail the course
- Be reported to the Center for Community Standards
- Have the right to appeal my decision
- Not be able to drop the course or withdraw from the course until the appeals process is finished
If you have any questions about what you can and cannot do in this course, ask me.
If you want to ask for a change in my decision about academic integrity, use the form at the Center for Community Standards website. You must submit this request within 21 calendar days of the decision.
University syllabus statement and link
Students are responsible for reading and understanding all university-wide policies and resources pertaining to all courses (for instance: accommodations, care resources, policies on discrimination or harassment), which can be found in the university syllabus.