Introduction to Structural Equation Modeling (SEM)

Lecturers: Eldad Davidov, Peter Schmidt & Yannick Diehl

Modality: Hybrid

Week 1: 10-14 August 2026

Workshop Contents and Objectives

Most quantitative methods used in survey research—regression, ANOVA, mediation analysis, and factor analysis—can be understood as special cases of one overarching framework: structural equation modeling (SEM).

In this intensive five-day course, you will learn to specify, estimate, and defend SEM models using your own data. We work with the open-source R package lavaan and its graphical interface lavaangui, where path diagrams, automatically generated code, and reproducible Quarto reports replace the manual workflows of earlier eras.

The course is structured in two parts. In the first part, we focus on measurement: building scales through confirmatory factor analysis (CFA), including bifactor, multitrait–multimethod, higher-order, and multiple-group models, as well as testing measurement invariance across groups and countries. In the second part, we move to full structural equation models with latent variables, covering formative and reflective indicators, mediation and indirect effects, moderation, and multiple-group SEM.

Cross-cultural and cross-group comparison is a central theme throughout. Visual clarity plays a key role: with lavaangui, complex models become intuitive path diagrams that you can read, modify, and discuss, while the corresponding lavaan code is generated automatically. The diagrams help you build intuition—you learn to think in models—while the syntax gives you the flexibility and precision to handle the full range of SEM applications. Conceptual input and hands-on work are closely integrated. Each method is introduced with examples and then applied—first to prepared datasets and, over the course of the week, to your own data. Participants are strongly encouraged to bring a dataset. Daily consultations and a final presentation session provide opportunities for direct feedback from instructors and peers. Practical exercises are conducted primarily in lavaangui, with lavaan code generated automatically—so you leave with fully reproducible scripts ready for your own projects. We also show how AI prompts can support model specification and how Quarto streamlines the path from analysis to publication-ready reports.

Participants who registered under the previous course description (using Amos) are welcome to continue working with it. Support will be provided through video materials and consultations. The course, however, will primarily focus on lavaan and lavaangui.

By the end of the course, you will be able to implement SEM confidently in your own research and produce fully reproducible analyses and publication-ready reports.

Workshop design

The workshop alternates between concise live or pre-recorded lectures, intuition-building exercises, and applied sessions in lavaangui, where you work hands-on with both prepared examples and your own data. Path diagrams generate lavaan code on the fly, making the connection between theory and statistical modeling transparent at every step.

Daily individual consultations and a final presentation session provide structured feedback and turn the workshop into a peer review of your own model

Deatiled lecture plan (daily schedule)

Day 1
Foundations: From theory to path diagrams—the logic of measurement models

Day 2
Confirmatory factor analysis (CFA): Building, testing, and refining scales

Day 3
Beyond standard CFA: Bifactor, multitrait–multimethod, higher-order, and multiple-group models—bridging to full SEM

Day 4
Structural equation modeling (SEM): Mediation, moderation, multiple-group models, and MIMIC

Day 5
Your turn: Participant presentations, peer feedback, and open clinic

See course outline below for details

Class materials

All materials will be provided online. The course will primarily use the R package lavaan (with lavaangui). Participants who registered under the previous course description indicating the use of Amos are welcome to continue working with it; support will be provided. 

Prerequisites

Some experience with regression analysis techniques is required. Basic knowledge of factor analysis is recommended. Participants who bring their own data will most profit from the course.

Recommended readings or preliminary material

Basic texts/overview

• Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press.
• Davidov, E., Schmidt, P., Billiet, J., & Meuleman, B. (Eds.). (2018). Cross-cultural analysis: Methods and applications (2nd ed.). Routledge.
• Gana, K., & Broc, G. (2019). Structural equation modeling with lavaan. Wiley.
• Kline, R. B. (2023). Principles and practice of structural equation modeling (5th ed.). Guilford Press.
  (Note: From this edition onward, all applications are also available in lavaan syntax.)
• Lammertyn, J. (n.d.). R syntax materials. Ghent University. GitHub repository.
• Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36. https://doi.org/10.18637/jss.v048.i02

Additional reading

• Aleman, J. A., Schmidt, P., Meitinger, K., & Meuleman, B. (2022). Editorial: Comparative political science and measurement invariance—basic issues and current applications. Frontiers in Political Science, 4, 1039744. https://doi.org/10.3389/fpos.2022.1039744
• Anderson, J. C., & Gerbing, D. W. (1988). Structural equation modeling in practice: A review and recommended two-step approach. Psychological Bulletin, 103, 411–423.
• Berry, W. D. (1984). Nonrecursive causal models. Sage.
• Cieciuch, J., Davidov, E., Schmidt, P., & Algesheimer, R. (2016). The assessment of cross-cultural comparability. In C. Wolf, D. Joye, T. W. Smith, & Y.-C. Fu (Eds.), The SAGE handbook of survey methodology (pp. 630–648). SAGE.
• Davidov, E., Cieciuch, J., Meuleman, B., Schmidt, P., & Billiet, J. (2014). Measurement equivalence in cross-national research. Annual Review of Sociology, 40, 55–75.
• Davidov, E., & Schmidt, P. (2007). Are values in the Benelux countries comparable? In G. Loosveldt, M. Swyngedouw, & B. Cambré (Eds.), Measuring meaningful data in social research (pp. 373–386). Acco.
• Davidov, E., Schmidt, P., & Schwartz, S. H. (2008). Bringing values back in: The adequacy of the European Social Survey to measure values in 20 countries. Public Opinion Quarterly, 72(3), 420–445.
• Davidov, E., Meuleman, B., Billiet, J., & Schmidt, P. (2008). Values and support for immigration: A cross-country comparison. European Sociological Review, 24(5), 583–599.
• Davidov, E., Seddig, D., Gorodzeisky, A., Raijman, R., Schmidt, P., & Semyonov, M. (2020). Direct and indirect predictors of opposition to immigration in Europe. Journal of Ethnic and Migration Studies, 46(3), 553–573.
• Heyder, A., & Schmidt, P. (2002). Authoritarianism and ethnocentrism in East and West Germany. In R. Alba, P. Schmidt, & M. Wasmer (Eds.), [Book title] (pp. 187–210). Palgrave Macmillan.
• Hoyle, R. H. (Ed.). (2023). Handbook of structural equation modeling (2nd ed.). Guilford Press.
• Knoppen, D., & Saris, W. (2009). Do we have to combine values in the Schwartz human values scale? Survey Research Methods, 3, 91–103.
• Leitgöb, H., Seddig, D., Asparouhov, T., Behr, D., Davidov, E., De Roover, K., Jak, S., Meitinger, K., Menold, N., Muthén, B., Rudnev, M., Schmidt, P., & van de Schoot, R. (2023). Measurement invariance in the social sciences. Social Science Research, 110, 102805.
• MacKinnon, D. P., Fairchild, A. J., & Fritz, M. S. (2007). Mediation analysis. Annual Review of Psychology, 58, 593–614.
• Meuleman, B., Żółtak, T., Pokropek, A., Davidov, E., Muthén, B., Oberski, D., Billiet, J., & Schmidt, P. (2022). Why measurement invariance is important. Sociological Methods & Research. https://doi.org/10.1177/00491241221091755
• Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7(2), 147–177.
• Schmidt, P., & Herrmann, J. (2011a). Factor analysis. In International encyclopedia of political science. SAGE.
• Schmidt, P., & Herrmann, J. (2011b). Structural equation models. In International encyclopedia of political science. SAGE.
• Steenkamp, J.-B. E. M., & Baumgartner, H. (1998). Assessing measurement invariance. Journal of Consumer Research, 25, 78–90.
• Steinmetz, H., Schmidt, P., Tina-Booh, A., Wieczorek, S., & Schwartz, S. H. (2009). Testing invariance using multigroup CFA. Quality & Quantity, 43, 599–616.
• Thompson, M. S., & Green, S. B. (2013). Evaluating between-group differences in latent variable means. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (pp. 163–218). IAP.
• Yang-Wallentin, F., Davidov, E., Schmidt, P., & Bamberg, S. (2004). Interaction effects between intention and perceived behavioral control. Methods of Psychological Research Online, 8(2), 127–157.
• Zick, A., Wolf, C., Küpper, B., Davidov, E., Schmidt, P., & Heitmeyer, W. (2008). The syndrome of group-focused enmity. Journal of Social Issues, 64(2), 363–383.

COURSE OUTLINE

The course shows how causal theories can be represented as path diagrams and translated into confirmatory factor models and full structural equation models (SEM), and how these models can be estimated and tested using lavaan in R.

In the first part, we focus on measurement models, linking single or multiple indicators to latent variables. Different specifications are introduced and evaluated using confirmatory factor analysis (CFA) as a special case of SEM.

In the second part, we move to full structural equation models that combine measurement and structural components. Topics include multiple-group modeling for cross-cultural data, MIMIC models, mediation, moderation, and the treatment of missing data. Special attention is given to model modification.

Participants are strongly encouraged to bring their own data. Time will be dedicated to individual consultations during the course, and participants will have the opportunity to present their models on the final day and receive feedback on their research.

Part 1: CONFIRMATORY FACTOR ANALYSIS

Day 1.
Overview of the whole course. Causality and empirical research, notation, different types of models, theory testing, use of Lavaan documentations, SEMNET and course material. Foundation of CFA: Process of linear causal modelling, types of input, assumptions, equality constraints, formalization, formative vs. reflective indicators, typology of models, treatment of missing values (pairwise vs. Full Information Maximum Likelihood - FIML).

Practical session: Lavaan and the logic of its use. CFA with one measurement model. Preparation of EXAMPLE 1: (input file: cov_NL2.sav). Conformity/Tradition (COTR) value with four indicators. Computation and interpretation of model 1. Model-Modification. Output interpretation and comparison of models.

Essential Reading:    Rosseel 2012; Brown 2015 chapter 3 and 7, 238-265; Davidov & Schmidt 2007, Schafer & Graham 2002, Schmidt & Hermann 2011 (a).

Additional reading:   Heyder & Schmidt 2002 (1-11); Gana & Broc 2019.

Day 2.
Restrictions, identification, model modifications, global and detailed model fit, Simultaneous Confirmatory Factor Analysis (SCFA).

Practical session: Preparation of EXAMPLES 2: (input File: cov_NL2.sav). SCFA and its modification: Conformity/Tradition and Universalism/Benevolence. Examination of detailed and global model fit. Types of errors, reliability and validity estimates in CFA, variance decomposition, Multiple Group Confirmatory Factor Analysis (MGCFA). Preparation of EXAMPLE 3: (Input Files: cov_NL2.sav, cov_BE2.sav, cov_LU2.sav). Multiple group comparisons across BENELUX countries.    

Essential Reading:    Brown 2015 chapters 3, 4, 5 and 7; Davidov, Meuleman, Billiet & Schmidt 2008;

Additional reading:  Davidov, Schmidt & Schwartz 2008; Davidov & Schmidt 2007; Knoppen & Saris 2009; Heyder & Schmidt 2002 11-13.

Day 3.
MGCFA with intercepts and latent means, higher order CFA, MTMM.

Practical session: EXAMPLE 4: (Input Files: cov_NL2.sav, cov_BE2.sav, cov_LU2.sav) MGCFA with means and intercepts: Subgroups Belgium, Netherlands, Luxemburg. Output interpretation.

Essential Reading:    Brown 2015 chapters 6, 7 and 8, Podsakoff et al. 2003, Steenkamp and Baumgartner 1998, Thompson & Green 2013.

Additional reading:   Leitgoeb et al. (2023); Meuleman et al.(2022); Steinmetz et al 2009;  Zick et al. 2008.

Part 2: STRUCTURAL EQUATION MODELS

Day 3.
Structural Equation Models (SEM) with latent variables and multiple indicators: Specification, identification and estimation. Causality and equivalent models. Typology of model testing. “The two step strategy“. Model Modification revisited. Theoretical exercise 6. 

Essential Reading:    Davidov et. al. 2008, Kline (2023, fifth edition, parts II to IV ) Schmidt & Hermann 2011 (b)

Additional Reading: Heyder & Schmidt 2002 (13-16); Anderson & Gerbing 1988.  

Day 4.
Model testing and model modification. Detailed and global fit measures. Interpretation of parameters. Feedback models. Decomposition of effects. Bootstrapping for testing indirect and total causal effects. Mediation. SEM with multiple groups: Model specification and estimation. MIMIC Models. Moderation/interaction effect (the Little method). MIMIC models with higher order factors, latent means and intercepts.

Practical session: SEM with decomposition of effects and mediation. Preparation of FINAL EXERCISE – READ ONLY (Input File: cov_NL2.sav): Full SEM and a MIMIC model: COTR, UNBE and sociodemographic variables. Using bootstrap to receive standard errors of indirect and total effects. Output interpretation.

Work on own data and consultation.

Essential Reading:    Heyder & Schmidt 2002 (17-23); MacKinnon et al. 2007; Davidov et. al. 2008; Kline(2023, parts II - IV); Schmidt & Herrmann 2011, Steinmetz et al. 2011.

Additional Reading: Berry 1984; Heyder & Schmidt 2002 (23-24); Yang-Wallentin et. al. 2006.

Day 5.
Participants’ presentations.

Essential Reading:    Brown 2015 chapter 9; Hoyle 2023 (selected chapters).

Further references

• Billiet, J. B., & Davidov, E. (2008). Testing the stability of an acquiescence style factor. Sociological Methods & Research, 36, 542–562.
• Bollen, K. A. (1989). Structural equations with latent variables. Wiley.
• Bollen, K. A. (2002). Latent variables in psychology and the social sciences. Annual Review of Psychology, 53, 605–634.
• Bollen, K. A. (2008). Frequently asked questions on structural equation models. The Sociological Methodologist, 6–8.
• Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. Wiley.
• Bollen, K. A., & Pearl, J. (2012). Eight myths about causality and structural equation models. In S. Morgan (Ed.), Handbook of causal analysis for social research. Springer.
• Boomsma, A. (2000). Reporting analyses of covariance structures. Structural Equation Modeling, 7(3), 461–483.
• Byrne, B. M., & Stewart, S. M. (2006). The MACS approach to testing multigroup invariance. Structural Equation Modeling, 13(2), 287–321.
• Curran, P. J., & Bollen, K. A. (2002). Combining autoregressive and latent curve models. In A. G. Sayer & L. M. Collins (Eds.), New methods for the analysis of change. APA.
• Davidov, E., Cieciuch, J., Meuleman, B., Schmidt, P., Algesheimer, R., & Hausherr, M. (2015). Comparability of attitudes toward immigration. Public Opinion Quarterly, 79(Special Issue), 244–266.
• Davidov, E., & De Beuckelaer, A. (2010). Testing equivalence of instruments. International Journal of Public Opinion Research, 22(4), 485–510.
• Davidov, E., Dülmer, H., Schlüter, E., Schmidt, P., & Meuleman, B. (2012). Multilevel SEM and measurement noninvariance. Journal of Cross-Cultural Psychology, 43, 558–575.
• Davidov, E., Schmidt, P., & Billiet, J. (Eds.). (2011). Cross-cultural analysis: Methods and applications. Routledge.
• Davidov, E., Thörner, S., Gosen, S., Schmidt, P., & Wolf, C. (in press). Latent growth curve models and group-focused enmity. Advances in Statistical Analysis.
• Duncan, T. E., & Duncan, S. C. (2009). The ABC’s of latent growth curve modeling. Social & Personality Psychology Compass, 3(6), 979–991.
• Duncan, T. E., Duncan, S. C., & Strycker, L. A. (2006). An introduction to latent variable growth curve modeling. Erlbaum.
• Finkel, S. (1995). Causal analysis with panel data. Sage.
• Hoogland, J. J., & Boomsma, A. (1998). Robustness studies. Sociological Methods & Research, 26(3), 329–367.
• Little, T. D., Slegers, D. W., & Card, N. A. (2006). Scaling latent variables. Structural Equation Modeling, 13, 59–72.
• MacKinnon, D. P., & Fairchild, A. J. (2009). Mediation analysis. Current Directions in Psychological Science, 18, 16–20.
• Podsakoff, P. M., MacKenzie, S. B., Lee, J.-Y., & Podsakoff, N. P. (2003). Common method bias. Journal of Applied Psychology, 88(5), 879–903.
• Saris, W. E. (2001). Measurement models in sociology. In R. Cudeck et al. (Eds.), Structural equation modeling: Present and future.
• Scherpenzeel, A. C., & Saris, W. E. (1997). Validity and reliability of survey questions. Sociological Methods & Research, 25, 347–383.
• Schlüter, E., Davidov, E., & Schmidt, P. (2007). Panel SEM models. In K. van Montfort et al. (Eds.), Longitudinal models in the behavioral sciences.
• Schumacker, R. E., & Lomax, R. G. (2010). A beginner’s guide to structural equation modeling (3rd ed.). Routledge.
• Sijtsma, K. (2009). On the misuse of Cronbach’s alpha. Psychometrika, 74(1), 107–120.
• Steinmetz, H., Davidov, E., & Schmidt, P. (2011). Latent interactions. Methodological Innovations, 6(1), 95–110.
• Vandenberg, R. J., & Lance, C. E. (2000). Measurement invariance review. Organizational Research Methods, 3(1), 4–70.
• Zercher, F., Schmidt, P., Cieciuch, J., & Davidov, E. (2015). Measurement invariance over time. Frontiers in Psychology, 6, 733.

 Relevant internet resources

• lavaan (R package): https://lavaan.ugent.be/
• lavaangui (graphical interface for lavaan): https://lavaangui.org/
• European Social Survey (ESS): https://www.europeansocialsurvey.org/
• SEMNET discussion group (mailing list): https://listserv.ua.edu/cgi-bin/wa?A0=SEMNET  

What our participants appreciated most

"The workshop was really helpful for my research. The facilitators were always open to questions and engaged with us in a respectful and approachable manner."

"Great instructors, clearly experts in the field."