Peter Schmidt is Professor emeritus at the department of political science and the Centre for Environment and Development of 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. Applications include studies of national identity, inter-ethnic relations, attitudes toward immigration, values and environmental behaviour. He has published several books and recently published in the Annual Review of Sociology, European Sociological Review, Journal for Ethnic and Migration Research, International Journal of Comparative Sociology, Journal for Cross-Cultural Psychology, Frontiers in Psychology, European Journal of Social Psychology, Psychological Methods, Structural Equation Modeling, Public Opinion Quarterly, Survey Research Methods and Sociological Methods and Research.   

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 the first part, we deal with confirmatory factor analysis (CFA), which relate multiple indicators to one (CFA) or several latent variables (Simultaneous Confirmatory Factor Analysis, Bifactor Models and second order 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 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 latent means. We also deal with the new procedures of measurement invariance testing (e.g., alignment optimization) as alternatives to check weak and strict 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 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 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 STATA_SEM and R lavaan..
3. to increase participants’ competencies in the applications of the techniques and models with their own data. Therefore, 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
B.Byrne(2012) Structural Equation Modeling with MPLUS, Routledge
R.B.Kline(2016) Principles and Practice of Structural Equation Modeling, Paperback, Fourth edition, Guilford Press
J.Wang/X.Wang (2019) Structural Equation Modeling: Applications Using Mplus. 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.
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
OLS = strong
Maximum Likelihood = elementary

Computer Background
MPlus = elementary


Day 1

Overview of the whole course. Comparative Data-Set (European Social Survey) and Type of Models. 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 MPLUS manual, MPLUS 8 additions, example from SEMNET and Discussion of the Course material. Use of own data. Presentation of own models and consultations.

Practical session : MPLUS and the logic of its use. Selected items and constructs: Values in the three Benelux countries. Confirmatory Factor Analysis (CFA) with one theoretical construct (factor). ML and MLR estimation Preparation of EXAMPLE 1: (input file: Benelux_nomissing.dat). Tradition and Conformity in the three Benelux countries with four indicators. Computation and Output Interpretation of model 1. Model-Modification. Comparison of factor loadings, measurement errors and global and detailed fit measures with ML and MLR.

Essential Reading: Brown, 2015 chapter 3; Byrne 2012, chapters 1 and 2; Davidov/Schmidt 2007; Muthén & Muthén 2012, chapter 1 and 2. Schwartz(2007,2012)

Additional reading: Davidov/Schmidt/Schwartz 2008; Marsh et. al. 2009.

Day 2

Foundation of CFA: Process of linear causal modelling, Raw Data as input, assumptions, Types of constraints including Equality constraints, formalization, formative vs. reflective indicators, typology of models, Maximum Likelihood Estimation (ML) and Robustified Maximum Likelihood Estimation (MLR). Ordinal Indicators and WLSMV Estimator.

Practical session : Preparation of CFA EXAMPLES 2a (parallel), 2b (tau-equivalent) and 2c (congeneric ordinal): (input file: NL2.dat). Output interpretation and comparison of quantitative and ordinal models in terms of fit, coefficients and explained variance. Optional: Example 2c with all Benelux countries(input file: Benelux_no missing.dat). Comparison of results.

Essential Reading: Brown 2006, chapters 4 and 7, 238-265; Byrne 2012, chapters 3, 4 and 5; Schmidt/Hermann 2011.

Additional Reading: Muthén & Muthén 2012, chapter 4,5. Davidov/Datler/Schmidt/Schwartz 2011

Day 3

Restrictions, Identification, Model Modifications, Global and Detailed Model Fit, Simultaneous Confirmatory Factor Analysis (SCFA) vs. Seperate Confirmatory Factor Analysis. Cross-Loadings and Measurement Error correlations. Model Modification with J-Rule and Power Analysis.

Practical session : Preparation of EXAMPLES 3a and 3b: (input File: NL2.dat). Simultaneous Confirmatory Factor Analysis and its modification: Tradition/Conformity, Universalism and Attitude toward immigration. Examination of detailed and global model fit.

Application of JRULE. Model Modification. Change in the Number of Factors, cross-loadings or measurement error correlations? Optional: Example 3b: SCFA for Belgium and Luxemburg (input File : Benelux_no missing.dat)

Essential Reading: Brown 2015, chapters 3, 4 and 5; Byrne 2012, chapters 3 and 4; Davidov/Schmidt/Schwartz 2008.

Additional reading: Davidov/Schmidt 2007; Marsh/Hau/Wen 2004; Muthén & Muthén 2012, chapter 4,5; Saris et. al. 2009; Saris/Knoppen 2009.   

Day 4

Multiple Group Confirmatory Factor Analysis (MGCFA). Configural, metric and scalar invariance in cross cultural research.Classical and new fit measures for testing invariance. The concept of partial invariance. The new Alignment procedure in MPLUS for comparisons of many groups(Fixed and Random)

Practical session : MGSCFA. Preparation of EXAMPLE 4a: (Benelux_noMissing.dat) Multiple group comparisons with the top down approach (MGCFA) due to BENELUX countries.

EXAMPLE 4b : CONFIGURAL METRIC SCALAR: the new procedure to perform a simultaneous test of measurement invariance (same input File) EXAMPLE 4c ALIGNMENT(Fixed and Random, ML ) as an alternative invariance testing procedure (same input File).

Essential Reading: Brown 2015, chapter 7; Byrne 2012, chapter 7; Ciechuch et al. 2016, Davidov 2008, Davidov et. al. 2008; Steinmetz et. al. 2009; Davidov et al. 2014; Davidov et al. 2015.

Additional Reading: Aspourov/Muthen 2014; Chen 2007; Davidov/De Beuckelaer 2010; Muthén & Muthén 2012, chapter 5; Munck et al. 2016, Marsh et al. 2016, Ciecuch et al. 2017

Day 5

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. Approximate Measurement Invariance and the Bayesian approach. Higher order CFA. General Strategy for testing measurement models in comparative research . How to report CFA results in comparative research.

Practical session : EXAMPLE 5: (Input Files: Benelux.dat) CFA with latent means: Subgroups Belgium, Netherlands, Luxemburg. Output interpretation. EXAMPLE 6: (same input File) Approximate Measurement Invariance and Bayesian estimation with a-priori information for estimating latent means.

Essential Reading: Brown 2015, chapters 6, 7 and 8; Byrne 2012, chapters 5, 8 and 10; Muthén & Muthén 2012, chapter 5; Van der Schoot et al. 2013; Ciecuch et al. 2014; Davidov et al. 2015.

Additional reading: Byrne/Stewart 2006; Davidov et. al. 2011; Davidov et al. 2014, 2015; Seddig et al. 2017; Steinmetz 2009; Zercher et al. 2015; Zick et al. 2008; McDonald et al. 2002.


Day 6

Structural Equation Models (SEM) with latent variables and multiple indicators: Specification, identification and estimation.The eight Matrices to represent the model. Multiple Group SEM.Causality and equivalent models. Typology of model testing. “The two step strategy“. Specification Search, Fit Measures and Model Modification revisited. Theoretical exercise 6.

Practical session : Preparation of a full SEM: Demographic Variables, Values and attitudes toward immigration.Example 6(Input File: Benelux.dat) MLR. Comparison of the results for the three countries for the separate analyses with unconstrained measurement models.

Essential Reading: Byrne 2012, chapter 6 ; Davidov et. al. 2008b; Schmidt/Hermann 2011.

Additional Reading: Anderson/Gerbing 1988; Kline 2011, chapters 6, 7 and 8; Muthén & Muthén 2012, chapter 5.

Day 7

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. Full and Partial Mediation in comparative analysis.

Practical session : Multiple Group SEM with decomposition of effects, feedback and mediation. Preparation of EXAMPLES 7a Feedback, 7b Indirect and total effects with Sobel test and bootstrap and 7c:Full versus partial Mediation (Input File: Benelux.dat) Output interpretation.

Essential Reading : Marsh et al.2004; Muthén & Muthén 2012, chapter 5; Muthen 2012 a.

Additional Reading: Paxton et al 2011; Mc-Kinnon 2006; Saris et al.2009, Bou & Satorra 2010. Muthen/Muthen/Aspourov 2016.

Day 8

Multiple group comparison and direct test of interaction effects, cross-cultural analysis and interaction effects/ moderation. Mediated Moderation. SEM with multiple groups: Model specification and estimation. Direct estimation of interaction effects with QML in Mplus. MIMIC Models. Differential Item Bias. MIMIC Models with higher order factors,

Practical session : SEM, multiple groups Moderation and MIMIC models of EXAMPLES 8a, 8b and 8c: (Input File: Benelux.dat, Benelux_noMissing.dat). MIMIC-Model Output interpretation. Example 8d(same Input File) Direct Estimation of Interaction(Moderation) Effects with QML in Mplus. Unstandardized and standardized effects.

Essential Reading: Byrne 2012, chapter 9; Davidov et. al. 2008b.

Additional Reading : Muthén & Muthén 2010, chapter 5; Davidov et. al. 2011; Davidov et al. 2014; Ganzeboom 2009; Yang-Wallentin et. al. 2006.

Day 9

Handling of Missing Values. Pairwise and Listwise Deletion. Full Information Maximum Likelihood Estimation and Multiple Imputation with Bayes in Mplus 7.4. Bayesian SEM for cross-cultural analysis. How to report SEM results.

Practical session : MIMIC-model with the additional causal factors and FIML estimation and Bayesian imputation : education, age and gender. Preparation of EXAMPLE 9a,b: (Input File: NL2.dat). Output interpretation.

Essential Reading : Byrne 2012, chapter 12; Muthén & Muthén 2010, chapter 6 and 11; Additional Reading: Kline 2011, 289-292 and 356-366; Schaefer/Graham 2002; Muthen/Aspourov 2012; Kuiper et al. 2013.

Day 10

Presentation of the SEM models of the participants using datasets from their projects. 15 minutes Power Point Presentation, 5 -10 minutes discussion of every presentation.

1. Methodological References

– Anderson, J. C. & Gerbing, D. W. (1988) Structural equation modeling in practice: A review and recommended two-step approach. Psychological Bulletin, 103(3), 411-423.

– Beierlein, C. & Davidov, E. & Schwartz, S. H. & Schmidt, P. & Rammstedt, B. (2012 – erscheint): Testing the discriminant validity of Schwartz‘ Portrait Value Questionnaire items: a replication and extension of Knoppen and Saris (2009). In Survey Research Methods 6(1), 25-36.

– Bollen, K. A. (2002). Latent Variables in Psychology and the Social Sciences. Annual Review of Psychology, 53, 605-634.

– Boomsma, A. (2000). Reporting analyses of covariance structures. Structural Equation Modeling, 7(3), 461-483.

– Brown, T.A. (2015) Confirmatory factor Analysis for Applied Research. Paperback Second Edition, Guilford.

– Byrne, B. M. & Stewart, S. M. (2006) The MACS Approach to Testing for Multigroup Invariance of Second-Order Structure: A Walk Through the Process, Structural Equation Modeling 13(2), 287-321.

– Byrne, B.M. (2012). Structural Equation Modeling with Mplus. Basic Concepts, Applications and Programming.

– Chen, F. F. (2007) Sensitivity of Goodness of Fit Indexes to Lack of Measurement Invariance, Structural Equation Modeling 14(3), 464-504.

– Ciecuch, J.& Davidov, E.& Schmidt, P.& Algesheimer,& S. Schwartz, S.(2014) Comparing results of an exact vs. an approximate (Bayesian) measurement invariance test: a cross country illustration with a scale to measure 19 values, Frontiers in Psychology,5, 59-68.

– Davidov, E. (2011) Nationalism and Constructive Patriotism: A Longitudinal Test of Comparability in 22 Countries with the ISSP. International Journal of Public Opinions. 23(1):, 88-103.

– Davidov, E. & De Beuckelaer, A. (2010) How Harmful are Survey Translations? – A Test with Schwartz´s Human Values Instrument, International Journal of Public Opinions Research, in Press

– Davidov, E. & Thörner, S. & Schmidt, P. & Gosen, S. & Wolf, C. (2011) Level and change of group-focused enmity in Germany: unconditional and conditional latent growth curve models with four panel waves. AStA Advances in Statistical Analysis. 95(4), 481-500.

– Davidov, E. & Datler, G. & Schmidt, P & Schwartz S. H. (2010) Testing the invariance of values in the Benelux countries with the European Social Survey: Accounting for ordinality. In: E. Davidov&P. Schmidt&J. Billiet (Eds.): Cross-Cultural Analysis: Methods and Applications (European Association of Methodology). Taylor and Francis, 2010

– Davidov,E. & Meuleman B.& Ciecuch J. & Schmidt P. & Billiet J. Equivalence in cross-national research, Annual Review of Sociology 2014.

– Davidov, E. &Ciecuch J.&Meulemann B.&Schmidt,P.& Algesheimer R.&Hausherr M.(2015) The comparability of Measurements of Attitudes toward Immigration in the European Social Survey, Public Opinion Quarterly, 79, 244-266.

– Hoogland, J. J. & Boomsma, A. (1998). Robustness studies in covariance structure modeling. An overview and a metanalysis. Sociological Methods & Research, 26(3), 329-367.

– Ganzeboom H. B. G. (2009) Multiple Indicators Models for social Background. Paper presented at European Survey Research Association, Warsaw, July 2009

– Kline,R. Structural Equation Modeling(2011), Third edition, Guilford.

– Marsh, H. W. & Muthén, B. & Asparouhov, T. & Lüdtke, O. & Robitzsch, A. & Morin, J. S. & Trautwein, U. (2009) Exploratory Structural Equation Modeling, Integrating CFA and EFA: Application to Students´ Evaluations of University Teaching. Structural Equation Modeling 16(3) 439 – 476.

– Marsh, H. W. & Hau, K. T. & Wen Z. (2004) In Search of Golden Rules: Comment on Hypothesis-testing Approaches to Setting Cutoff Values for Fit Indexes and Dangers in Overgeneralizing HU and Bentler´s (1999) Finings. Structural Equation Modeling 11(3) 320- 341.

– Marsh, H.W.(2016)

– Muller, D. & Judd, C. M. & Yzerbyt, V. Y. (2005) When Moderation Is Mediated and Mediation Is Moderated. Journal of Personality and Social Psychology. 89 (6), 852–863.

– Muthén, L. K. & Muthén, B. O. (2012) MPLUS – Statistical Analysis With Latent Variables User’s Guide. Muthén & Muthén

– Muthén, B. O. (2011) Applications of Causally Defined Direct and Indirect Effects in Mediation Analysis using SEM in Mplus. Muthén & Muthén

– Preacher, K. J. & Kelley, K. (2011) Effect size measures for mediation models: Quantitative strategies for communicating indirect effects. Psychological Methods. 16 (2), 93-115.

– Saris, W. E. (2001). Measurement models in sociology and political science. In Structural Equation Modeling: present and future. Robert Cudeck, Stephen Du Toit, Dag Soerbom, editors.

– Saris, W. E. & Satorra, A. & van der Veld, W. M. (2009) Testing Structural Equation Models or detection of Misspecifications? Structural Equation Modeling 16(4) 561- 582.

– Schafer, J. L. & Graham, J. W. (2002): Missing Data: Our View of the State of the Art. Psychological Methods. (7(2)) 147–177.

– Scherpenzeel, A.C. & Saris, W. E. (1997). The validity and reliability of survey questions. In Sociological Methods and Research, 25, 347-383.

– Schmidt, P. & Herrmann, J. (2011). Factor Analysis, in International Encyclopedia of Political science Methodology, Sage.

– Schmidt, P. & Herrmann, J. (2011). Structural Equation Models in : International Encyclopedia of Political science Methodology, Sage.

– Sijtsma K. (2009) On the Use, the Misuse, and the very limited Usefulness of Cronbach´s Alpha. Psychometrika 74(1) 107- 120.

– Steinmetz, H. & Schmidt P. & Tina-Booh A. & Wieczorek S. & Schwartz S. H.(2009). Testing invariance using multigroup CFA: differences between educational groups in human values measurement, Quality and Quantity, 599-616.

– Steinmetz, H. & Davidov, E. & Schmidt, P. (2011). Three Approaches to Estimate Latent Interaction Effects: Intention and Perceived Behavioral Control in the Theory of Planned Behavior. Methodological Innovations Online. 6(1), 95-110.

– Van de Schoot, R.& Kluytmans A.&,Tummers,L.& Lugtig,P.& Hox, J.&Muthen,B. Facing off Scylla and Charybdis: a comparison of scalar, partial and the novel possibility of approximate invariance, Frontiers in Psychology ,5, 173 – 187.

– Van der Schoot, R.&Schmidt,P.& Beuckelaer, A.(2015) Measurement Invariance, Special Issue in Frontiers in Psychology, 5.

– Yang-Wallentin, F., Davidov, E., Schmidt, P. &/ Bamberg, S.: Is there any interaction effect between intention and perceived behavioral control?, Methods of Psychological Research Online 2004, 8(2), 127-157.

– Zercher,F.&Schmidt,P.&Ciecuch, J.& Davidov E.(2015) The comparability of the universalism value over time and countries in the European Social Survey: exact vs. approximate invariance, Frontiers in Psychology , 6.733 doi:10.3389/fpsyg.2015.00733

2. Substantive References

– Davidov, E. & Schmidt, P. (2007). Working Paper: Are values in the Benelux countries comparable? Testing for equivalence with the European Social Survey 2004-5.

– 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. (2008b). Values and Support for Immigration: A Cross-Country Comparison. European Sociological Review – Oxford Univ Press. 24(5). 583-599.

– Knoppen.D. & Saris,W. (2009) Do we have to combine values in the Schwartz ` Human Values Scale? A Comment on the Davidov Studies. Survey Research Methods, 3, 91-103.

– Wagner, U. & Becker, J. C. & Christ, O. & Pettigrew T. F. & Schmidt, P. (2010) A Longitudinal Test of the Relation between German Nationalism, Patriotism, and Outgroup Derogation. European Sociological Review, 1-14

– Zick, A. & Wolf, C. & Küpper, B. & Davidov, E. & Schmidt, P. & Heitmeyer W. (2008). The Syndrome of Group-Focused Enmity: The Interrelation of Prejudices Tested with Multiple Cross-Sectional and Panel Data. Journal of Social Issues, 64 (2), 363-383.

3. Relevant internet homepages:

– concerning the MPLUS software:

– concerning the ESS data:

– concerning joining the SEMNET

discussion group: