Please note: This course will be taught online only. In person study is not available for this course.
Peter Schmidt is Professor Emeritus at the Department of Political Science and the Centre of International Development and Environment (ZEU) at the University of Giessen. His research interests are the foundations and applications of structural equation models, methods for cross-cultural analysis, analysis of panel data, and empirically testing wide versions of rational choice theory like the reasoned action approach and value research. Substantive work is dealing mainly with Attitudes toward migration and refugees, authoritarianism and prejudice and environmental behaviour. .
Recent publications
• Pokropek, A., Zoltak T., Davidov, E. Meuleman, B., Schmidt, P. (2025) Challenges in Multilevel Modeling : Cross-Group Measurement Invariance and Measurement Errors. A Monte Carlo Simulation Study. Sociological Methods and Research, https://doi.org/10.1177/00491241251379459.
• Meuleman, B.; Abts, K., Schmidt, P., Pettigrew, T., & Davidov, E. (2020). Economic Conditions, group relative deprivation and ethnic threat perceptions: a cross-cultural perspective. Journal of Ethnic and Migration Studies 46(3), 593 – 611.
• Bamberg, S.,Schmidt,P., Diehl, Y.,Hamilton, K., Aizen, I.(2025) The theory of reasoned goal pursuit: An empirical test in the domain of avoiding single-use plastic packaging, Journal of environmental psychology. https:// doi.org/ 10.1016/j.jenvp.2025.102698.
Daniel Seddig, PhD, is a Sociologist and Head of the Methods Section at the Criminological Research Institute of Lower Saxony (Kriminologisches Forschungsinstitut Niedersachsen, Hannover, Germany). His research interests are cross-cultural and longitudinal studies of human values, attitudes, and behavior, and their connection to social issues such as crime, trust in democratic and legal institutions, health, gender roles, and immigration. His methodological expertise is the analysis of longitudinal and comparative data using structural equation modeling. He is currently president of the European Survey Research Association (ESRA) and chair of the European Working Group on Quantitative Methods in Criminology in the European Society of Criminology (ESC).
Recent publications
• Seddig, D. (2024). Assessment of the dimensionality and comparability in legal cynicism measurement. Justice Quarterly, 1–26. https://doi.org/10.1080/07418825.2024.2393197
• Seddig, D. (2024). Latent growth models for count outcomes: Specification, evaluation, and interpretation. Structural Equation Modeling, 31 (1), 182- 198 https://doi.org/10.1080/10705511.2023.2175684
• 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: Historical development, methodological challenges, state of the art, and future perspectives. Social Science Research, 102805. https://doi.org/10.1016/j.ssresearch.2022.102805
Course Content
The course shows how theoretical assumptions concerning measurement models and substantive models can be translated into a structural equation model, and how the model can be estimated and tested using the R programming environment. In addition, we provide syntax for all examples in Mplus. We will show how to convert R-lavaan code into Mplus code and vice versa.
In the first part, we deal with confirmatory factor analysis (CFA), which relates multiple indicators to one (CFA) or several latent variables (Simultaneous Confirmatory Factor Analysis, Bifactor Models and second order confirmatory factor analysis) and multiple-group confirmatory factor analysis. Different specifications of measurement models are tested via confirmatory factor analysis (CFA) as a special case of a structural equation model (SEM) and we will discuss scale building procedures, measurement invariance testing and adequate reliability and validity estimates.
Special emphasis is given to the (cross cultural) analysis of multiple groups (MGCFA) for comparisons between groups and over time points (repeated cross-sections), including the assessment of measurement invariance (i.e., comparability of intercepts of observed variables and factor loadings) to compare regression coefficients and latent means. We also deal with the new procedures of measurement invariance testing (e.g., alignment optimization) to check approximate measurement invariance.
The second part comprises both the structural model and the measurement model. Topics include recursive vs. non-recursive models for the structural part of the model, the use of formative vs. reflective indicators in MIMIC models, mediation and effect decomposition, moderation (interaction effects), and treatment of missing and categorical data. Again, special emphasis will be directed toward the use of the multiple-group option for cross-group comparisons of both the measurement and the structural model. A major focus will be the process of model modification and alternative model testing using adequate fit measures and how to report CFA and SEM results.
We will draw all examples are from data of the European Social Survey (ESS) and use the concept of human values as operationalized by the Portrait Value Questionnaire developed by Schwartz for single country or cross-cultural analyses. Nonetheless, participants from all fields are welcome to participate.
Course Objectives
The objectives of this course are:
1.to enable participants to use (multiple group) confirmatory factor analysis and (multiple group) structural equation modelling to develop and/or test both measurement models and scales and, furthermore, causal theories with latent variables.
2. to familiarize participants with the lavaan-package in the R programming environment to handle the most important standard models. Nonetheless, to facilitate the transfer of the course content to other programs, all example syntaxes will also be supplied for Mplus.
3. to increase participants’ competencies in the applications of the techniques and models with their own data, participants are highly encouraged to bring their own data as cleaned raw data files (see for input specifications of the data, e.g., Byrne 2012) and to use them for developing their models and projects for a dissertation or publications during the course. We will offer consultation hours from the beginning both by the instructor and the teaching assistant to answer individual questions and specially to support participants to perform analyses with their own data. Moreover, we will offer an open colloquium format to present and critically discuss the own research findings.
Course Prerequisites
Participants are expected to have extensive familiarity with Windows applications, good knowledge of exploratory factor analysis and regression analysis is required. The course is most optimal for those who want to apply CFA and SEM within the next twelve months.
Remedial Reading
• T. Brown (2015) Confirmatory Factor Analysis for Applied Research, Paperback, Second edition, Guilford Press
• R.B. Kline (2016) Principles and Practice of Structural Equation Modeling, Paperback, Fourth edition, Guilford Press
• B. Byrne (2012) Structural Equation Modeling with MPLUS, Routledge
• J. Wang and X. Wang (2019) Structural Equation Modeling: Applications Using Mplus. J.Wiley.
• K. Gama and G. Broc (2019) Structural Equation Modelling with lavaan. New York, J. Wiley
Representative Background Reading
• E.Davidov/P.Schmidt/S.Schwartz(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.
• E.Davidov/B.Meuleman/J.Billiet/P.Schmidt(2008) Values and the Support for immigration: A Cross Country Comparison, European Sociological Review,24,5,583-599.
• E.Davidov/P.Schmidt/J.Billiet and B.Meuleman(April 2018) Cross-Cultural Analysis,: Methods and Applications. Paperback.Routledge
• E.Davidov/B.Meulemann/J.Ciechuch/P.Schmidt/J.Biliet(2014) Measurement Invariance in cross-national research, Annual Review of Sociology, 40, 55-75.
Background Knowledge Required
Statistics
OLS – moderate
Maximum Likelihood – elementary
Software
R – elementary
Maths
Calculus – elementary
Linear Regression – moderate
Week 1: CONFIRMATORY FACTOR ANALYSIS for COMPARATIVE RESEARCH
Generally
In the practical exercises, we will focus exclusively on the software R-lavaan. In addition, we provide syntax for all examples in Mplus. We will show how to use R procedures that produce lavaan code from Mplus input (mplus2lavaan) and Mplus input, Mplus compatible data and output via R (MplusAutomation). In case you have your own data available, we strongly encourage you to use them and work with them over the course of the summer school. We offer time for individual consultations concerning your data and projects and we incorporate presentations of your own models and findings at the end of the course.
DAY 1
Theory and illustration: Types of models, causality and data-dets
Overview of the whole course. Types of models, comparative dataset (European Social Survey) and the concept of values in the ESS. Causality and empirical research, notation, the generalized latent variable model and different types of models, theory testing, use of the r-lavaan tutorial and transformation of R-lavaan code into Mplus syntax. Use of AI to produce R-lavaan syntax. Discussion of the course material.
Practical exercise: CFA with one construct and three indicators
R-lavaan and the logic of its use, preparing and reading-in data into R-lavaan Selected items and constructs: values and attitudes in the three Benelux countries. Confirmatory factor analysis (CFA) with one theoretical construct (factor): tradition and conformity in the Netherlands with four indicators.
Essential Reading: Brown (2015), chapter 3.
Additional reading: Byrne (2012), chapters 1 and 2; Davidov & Schmidt (2007); Davidov, Schmidt, & Schwartz (2008); Rosseel (2012, 2025); Schwartz (2007, 2012).
DAY 2
Theory and illustration: CFA model specification, estimation and model fit
Foundation of CFA: linear causal modelling, raw data as input, assumptions, types of constraints including formalization, equality constraints. Maximum likelihood estimation (ML) and robust maximum likelihood estimation (MLR). Global and detailed model fit. Ordinal indicators and weighted least squares (WLSMV) estimation. List of presentations of individual projects on Day 10.
Practical exercise: Simultaneous CFA with two constructs and model fit
Modelling the values tradition and conformity in the Netherlands with four indicators, estimation and output interpretation. Estimation of 2-factor models. Comparison of factor loadings, measurement errors. Using global and detailed model fit and model modification statistics with ML and MLR.
Essential Reading: Brown (2015), chapters 4 and 7, 207-241.
Additional Reading: Byrne (2012), chapters 3, 4 and 5; ; Davidov, Datler, Schmidt, & Schwartz (2011); Schmidt & Hermann (2011).
DAY 3
Theory and illustration: Simultaneous confirmatory factor analysis, restrictions and identification, comparison of model fit
Equality constraints. Restrictions, identification, simultaneous confirmatory factor analysis (SCFA) vs. separate confirmatory factor analysis, cross-loadings and measurement error correlations. Comparison of model-fit measures and cut-off values.
Practical exercise: Test theory models and simultaneous confirmatory factor analysis with three constructs
CFA with tau-equivalent, parallel and strictly parallel constraints. Output interpretation and comparison of model fit, coefficients and explained variance. SCFA and its modification: tradition/conformity, universalism and attitude toward immigration. Examination of detailed and global model fit.
Essential Reading: Brown (2015), chapters 3, 4 and 5.
Additional reading: Byrne (2012), chapters 3 and 4; Davidov & Schmidt (2007); Davidov, Schmidt, & Schwartz (2008); Marsh et al. (2004); Muthén & Muthén (2012), chapters 4 and 5; Saris et al. (2009); Saris & Knoppen (2009).
DAY 4
Theory and illustration: Multi-group confirmatory factor analysis (MGCFA) and measurement invariance (MI)
Multiple group confirmatory factor analysis (MGCFA). Configural, metric and scalar invariance in cross cultural research. Classical and new fit measures for testing measurement invariance. The concepts of partial invariance and alignment.
Practical exercise: MGCFA and MI in the Benelux countries
MGCFA by hand. Multiple group comparisons with the bottom-up approach and the top down approach (MGCFA) across Benelux countries. Using the Mplus convenience feature for a simultaneous test of measurement invariance. Introduction of partial measurement invariance.
Essential Reading: Brown (2015), chapter 7, 241-284.
Additional Reading: Asparouhov & Muthen (2014); Byrne (2012), chapter 7; Chen (2007); Ciechuch et al. (2016, 2017); Davidov (2008); Davidov et al. (2008); Davidov & De Beuckelaer (2010); Davidov et al. (2014); Davidov et al. (2015); Kotzur et al., (2019); Marsh et al. (2016); Munck et al. (2016); Muthén & Muthén (2012), chapter 5; Steinmetz et al. (2009)
DAY 5
Theory and illustration: Scalar invariance and latent means. Higher order MTMM and bifactor models
Scalar invariance in cross cultural research as a prerequisite of comparing observed and latent means. Mean comparisons of items, indices and latent variables. Drawbacks of the t-test. Using the new alignment procedure in R-lavaan and Mplus as an alternative invariance testing procedure for comparisons of many groups (fixed and random). Higher order CFA and bifactor Models. General strategy for testing measurement models in comparative research. How to report CFA results in comparative research.
Practical exercise: CFA with latent means.
CFA with latent means, output interpretation, consolidation of the contents of the first week. Optional: Alignment optimization.
Essential Reading: Brown (2015), chapter 8.
Additional reading: Byrne (2012), chapters 5, 8 and 10; Byrne & Stewart (2006); Ciecuch et al. (2014); Davidov et al. (2011); Davidov et al. (2014, 2015); Lomazzi & Seddig (2020); McDonald et al. (2002); Muthén & Muthén (2012), chapter 5; Reise et al. 2017; Seddig et al. (2020); Steinmetz et al. (2009); Van der Schoot et al. (2013); Zercher et al. (2015); Zick et al. (2008).
Week 2: STRUCTURAL EQUATION MODELS
DAY 6
Theory and illustration: the “full” structural equation model
Path modeling foundations and structural equation models (SEM) with latent variables and multiple indicators: specification, identification, and estimation. Additional topics: model fit and model modification revisited, two-step approach.
Practical exercise: Values and attitudes toward immigration
Preparation of a full SEM: demographic (control) variables, human values and attitudes toward immigration. Comparison of the results for the three countries for the separate analyses with (un)constrained measurement models.
Essential Reading: Kline (2016), chapters 6, 7 and 8 (DAY 6 & 7).
Additional Reading: Anderson & Gerbing (1988); Davidov et al. (2008b); Saris et al. (2009); Schmidt & Hermann (2011).
DAY 7
Theory and illustration: mediation and the decomposition of effects
Specification, estimation, and interpretation of mediation models, decomposition of effects, bootstrapping for testing indirect and total effects; additional topic: “structural after measurement (SAM)” approach.
Practical exercise: values and attitudes toward immigration
Full SEM with decomposition of effects into indirect and total effects with the Sobel test and bootstrapping, full versus partial mediation, output interpretation.
Essential Reading: Kline (2016), chapters 6, 7 and 8 (DAY 6 & 7).
Additional Reading: Gonzalez et al. (2023); Rosseel & Loh (2024); Seddig et al. (2022).
DAY 8
Theory and illustration: Moderation in SEM
Testing moderation with multiple group structural equation modeling (MGSEM). Estimation of interaction effects in SEM using the product indicator, latent moderated structural equations, or quasi maximum likelihood approaches (modsem-package in R).
Practical exercise: age as moderator of the effect of values on attitudes toward migration
Using several approaches in R-lavaan.
Essential Reading: Kline (2016), chapters 6 (133-135) and 17.
Additional Reading: Ganzeboom (2009); Kelava & Brandt (2023); Rosseel et al. (2025); Yang-Wallentin et al. (2006).
DAY 9
Theory and illustration: categorical data analysis
Handling of missing values (pairwise/listwise deletion and full information maximum likelihood estimation); analyzing categorical data with R-lavaan.
Practical exercise: Preparation for individual presentations on Friday.
Essential Reading: Kline (2016), 83-87; 237-238; 458-460; Edwards et al. (2012).
Additional Reading: Schaefer & Graham (2002).
DAY 10
Presentation of results of participants
Presentation of the SEM models of the participants using datasets from their projects. 15 minutes presentation, 5-10 minutes discussion for every presentation.
