**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 and P.I. and Research Associate at the Department of Psychosomatic Medicine of the University of Mainz. 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.

Recent Publications:

Pokropek, A.,Davidov, E. &Schmidt, P. (2019) A Monte Carlo Simulation Study to assess the appropriateness of traditional and newer approaches to test for measurement invariance, Structural Equation Modeling, 26(5) 724-744

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.

Sok, J., Borges, J.R., Schmidt, P. & Aizen, I. (2021) Farmer Behavior as reasoned action: a critical review of research with the theory of planned behavior, *Journal of Agricultural Economics*, 72(2), 388 – 412.

**Daniel Seddig** is a senior researcher at the Institute of Sociology and Social Psychology at the University of Cologne and currently interims professor for criminology at the University of Münster. His research interests are social behaviors, behavioral intentions, and attitudes on health, crime and immigration, political orientations, cultural and personal values, and socio-economic/demographic disparities. He uses structural equation modeling for comparative and longitudinal analysis of quantitative data.

Recent publications:

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. (2022). Measurement invariance in the social sciences: Historical development, methodological challenges, state of the art, and future perspectives. *Social Science Research*, 102805. DOI: 10.1016/j.ssresearch.2022.102805

Seddig, D., Maskileyson, D., Davidov, D., Ajzen, I., & Schmidt. P. (2022). Correlates of COVID-19 vaccination intentions: Attitudes, institutional trust, fear, conspiracy beliefs, and vaccine skepticism. *Social Science and Medicine*, *302*, 114981. DOI:10.1016/j.socscimed.2022.114981

Seddig, D., Maskileyson, D., Davidov (2022). Vaccination against COVID-19 reduces virus-related fears: Findings from a German longitudinal study. *Frontiers in Public Health, 10*, 878787. DOI: 10.3389/fpubh.2022.878787

**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 with the Mplus 8 computer program. In addition, we provide syntax for all examples in R (lavaan). 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 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, moderation (interaction effects) and mediation analyses, treatment missing and categorical data and the use of formative vs. reflective indicators in MIMIC Models. 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 Mplus 8 program 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 R lavaan..

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 –

**this text will be provided by ESS**

R.B. Kline (2016) Principles and Practice of Structural Equation Modeling, Paperback, Fourth edition, Guilford Press – **this text will be provided by ESS**

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

**Computer Background**

R = elementary

MPlus = elementary

*Maths*

Calculus = elementary

Linear Regression = moderate