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Introduction to Structural Equation Modelling

Course Dates and Times

Monday 29 July – Friday 2 August and Monday 5 – Friday 9 August

09:00–10:30 & 11:00–12:30

Jochen Mayerl

Technische Universität Chemnitz

The course is an introduction to the theory and practice of Structural Equation Modelling (SEM).

It shows how theoretical latent constructs (e.g. social and political attitudes, values, and intentions) can be operationalized, and their causal relationships tested.

The course introduces the logic of SEM on a general level and shows how to use specialised computer software like R (package lavaan), Mplus and AMOS.

Week 1 introduces the specification of Confirmatory Factor Analysis (CFA) as a special case of SEM. Measurement models with single or multiple indicators of latent variables are estimated and tested. Different modelling specifications will be introduced including multiple group analysis (e.g. to test measurement equivalence across different social groups or countries).

Week 2 deals with specification and test of causal structural equation models (e.g. MIMIC models (Multiple Indicators and Multiple Causes), assessment of models, mediation and moderation, feedback loops).

ECTS Credits for this course, and below, tasks for additional credits:

6 credits Complete a take-home exam or a take-home paper

8 credits Complete the take-home exam and the take-home paper

Instructor Bio

Jochen Mayerl has been a researcher and lecturer in empirical methods of Social Sciences at University of Kaiserslautern since March 2013.

From November 2001 to February 2013, he lectured in Sociology and empirical social research at the University of Stuttgart, where he has taught various research and analysis methods. He finished his doctoral thesis, Cognitive foundations of social behaviour: theoretical and statistical analysis of attitude-behaviour relations, in 2008. During the winter term 2011/2012, he was substitute professor at the University of Kassel, Germany.

His main research interests in methodology are new developments and applications in structural equation modelling, response effects in surveys, and response latency measurement in computer assisted surveys.

He has published in the field of methodology as well as sociological theory (attitude-behaviour research, bounded rationality, framing) and substantial research (e.g. donation behaviour, environmental concern, ethnocentrism, political attitudes).

Structural Equation Modelling (SEM) is a powerful tool to analyse latent variable models common in social sciences, e.g. the analysis of personality factors, social and political attitudes, social values, and behavioural intentions.

SEM combines factor analysis and path analysis by simultaneously estimating causal relations between latent constructs and relations of latent constructs and their corresponding manifest indicators in the measurement models. SEM also allows the estimation and control for random and systematic measurement errors. Thus, SEM methodology allows an adequate modelling and empirical testing of measurement models and complex theoretical assumptions.

The course introduces the theory and practice of SEM on a general level. It does not stick to a specific computer software; rather, different software packages will be shown, used and compared, including R (package lavaan), Mplus and AMOS.

Basic modelling techniques of SEM are explained and applied by exercises using free access social science data. I encourage you to use your own data for analyses. Exercises allow the application and transfer of SEM methodology to your own research interests.

First week

I introduce principles of Structural Equation Modelling. I show how Confirmatory Factor Analysis (CFA) can be specified and estimated, i.e. how latent constructs (e.g. attitudes, values, behavioural intentions) can be operationalised by multiple manifest indicators and how these measurement models can be tested empirically.

Day 1
A general introduction to the advantages, possibilities, and applications of SEM and its relations to Principal Component Analysis (PCA). Regression analysis and path analysis are shown and discussed. I introduce basic concepts like manifest and latent variables, measurement model and structural model, formative and reflective indicators, and relation of modelling and theory.

Day 2
I introduce basic principles of SEM (e.g. causality and theory testing, notation, assumptions, formalisation, estimation procedures, model specification, model identification). I show how a Confirmatory Factor Analysis (CFA) can be estimated to operationalise latent constructs specifying measurement models with manifest indicators (multiple-indicator models). We discuss data and modelling ideas for participants’ own projects.

Day 3
How to identify ‘good’ CFA models, i.e. the interpretation of fit indices. I show how to specify, estimate, assess and re-specify a CFA model step-by-step (model modification). Preconditions like normality and outlier identification will be evaluated, and I demonstrate the specification of higher order constructs to measure multidimensional latent constructs. I show how to deal with systematic measurement errors (e.g. error correlations and specification of method factors) and how to estimate one-indicator measurement models. I introduce validity and reliability estimates in CFA.

Day 4
Multiple group analysis is a very important and powerful tool for comparative social science. I show how multiple group models can be specified, estimated and evaluated to test for measurement equivalence of different groups (e.g. within and between social groups, sub-populations, countries).

Day 5
Multiple group models are extended to the specification of a CFA with meanstructure, i.e. with latent means and intercepts. This lets us estimate and compare latent means between different groups and countries. We will discuss possible problems of models with meanstructure.

Second week

We introduce full SEM to specify and estimate causal relations between latent constructs and thus to test theoretical hypotheses. I will illustrate and discuss advanced techniques of SEM, and highlight special problems.

Day 6
This day deals with the specification of full causal structural equation models. We discuss alternative modelling strategies and equivalent causal models. I also show how to specify, estimate and interpret MIMIC (Multiple Indicators and Multiple Causes) models.

Day 7
I introduce decomposition of causal effects, model modification and interpretation of parameters. I show how to estimate direct, indirect and total effects and how to estimate their standard errors and significance (models with intervening latent variables). Thus, I demonstrate how to test for mediation effects. I show how to specify and estimate non-recursive models (models with feedback loops) and how to handle their particular problems.

Day 8
Full SEM is extended to multiple group comparison to test for moderator effects (and combined moderator-mediator models). We extend full SEM to full SEM with meanstructure, i.e. with latent means and intercepts. We discuss issues of standardisation and sample size in SEM.

Day 9
We discuss special topics of SEM, including its the logic and specification with categorical indicators and non-normal data (e.g. bootstrapping), strategies for dealing with missing values, and how to specify non-linear effects. I introduce interaction models as an alternative to multiple group analysis, and I show how to specify formative measurement models.

Day 10
Time for open questions and a chance for students to present their own models. I introduce advanced models e.g. panel models like cross-lagged autoregressive models and latent growth curve models, and advise on best practice when reporting SEM results. Our final discussion deals with problems and possible traps of SEM.

You should understand the basic principles of regression analysis and the meaning of regression results.

Basic understanding of principal component analysis (exploratory factor analysis) would be helpful.

You should be familiar with software to manage data, such as SPSS, STATA and R.

Each course includes pre-course assignments, including readings and pre-recorded videos, as well as daily live lectures totalling at least two hours. The instructor will conduct live Q&A sessions and offer designated office hours for one-to-one consultations.

Please check your course format before registering.

Online courses

Live classes will be held daily for two hours on a video meeting platform, allowing you to interact with both the instructor and other participants in real-time. To avoid online fatigue, the course employs a pedagogy that includes small-group work, short and focused tasks, as well as troubleshooting exercises that utilise a variety of online applications to facilitate collaboration and engagement with the course content.

In-person courses

In-person courses will consist of daily three-hour classroom sessions, featuring a range of interactive in-class activities including short lectures, peer feedback, group exercises, and presentations.


This course description may be subject to subsequent adaptations (e.g. taking into account new developments in the field, participant demands, group size, etc.). Registered participants will be informed at the time of change.

By registering for this course, you confirm that you possess the knowledge required to follow it. The instructor will not teach these prerequisite items. If in doubt, please contact us before registering.

Day Topic Details
1 Introduction to SEM

3 hours lecture and exercises

2 Basic principles of SEM; Confirmatory Factor Analysis (CFA); measurement models

90 minutes lecture – 90 minutes exercises

3 Fit Indices; CFA: step by step; test of normality & outliers; second order measurement models; method factors

90 minutes lecture – 90 minutes exercises

4 Multiple Group CFA: testing measurement equivalence

90 minutes lecture – 90 minutes exercises

5 Multiple Group CFA: Latent means

90 minutes lecture – 90 minutes exercises

6 Full SEM; model testing strategies; MIMIC models

90 minutes lecture – 90 minutes exercises

7 Mediation, decomposition of causal effects: direct, indirect and total effects; feedback loops

90 minutes lecture – 90 minutes exercises

8 Multiple group SEM and moderation, SEM with meanstructure; sample size in SEM

90 minutes lecture – 90 minutes exercises

9 Special topics of SEM: categorical indicators and non-normality (incl. bootstrapping); interaction effects; missing value treatment; nonlinearity; formative measurement models

90 minutes lecture – 90 minutes exercises

10 Open questions and presentation of participants' models; Advanced techniques (e.g. cross-lagged autoregressive models, latent growth curve models); Discussion ('overfitting', how to fool yourself with SEM); How to report SEM results

90 minutes lecture – 90 minutes exercises

Day Readings

Byrne 2016: chapter 1 and 2 (introduction to SEM)


Byrne 2016: chapter 3 (CFA);
Additional reading Kline 2016: chapter 9 (specification), 10 (identification) and 11 (pp 231-239 ML estimation)


Byrne 2016: chapter 4 (CFA) and 5 (second order CFA)
Additional reading Kline 2016: chapter 12 (fit indices), 13 (CFA)


Byrne 2016: chapter 7 (multigroup CFA)
Additional reading Kline 2016: chapter 16 (multigroup CFA)


Byrne 2016: chapter 8 (multigroup CFA with meanstructure)
Additional reading Kline 2016: chapter 15 (pp 369-374; meanstructure)


Byrne 2016: chapter 6 (full SEM)
Additional reading Kline 2011: chapter 10


Maruyama 1998: pp. 35-48 (effect decomposition);
Kline 2016: pp. 239-253 (effect decomposition), pp. 150-157 (non-recursive models)


Byrne 2016: chapter 9 (multigroup full SEM)


Byrne 2016: chapter 12 (bootstrapping) and 13 (missing data);
Additional reading Kline 2016: chapter 17 (interaction effects);
Ping 1996 (interaction effects); Schafer/Graham 2002 (missing data)


Kline 2011: chapter 13 (How to fool yourself with SEM);
Kline 2016: chapter 18 (best practices);
Boomsma 2000 (reporting SEM results)

Software Requirements

Download trial version of IBM SPSS Amos 24

R (version 3.5.2 or higher) with RStudio Desktop (version 1.1.463 or higher) and R packages: (lavaan version 0.6-30 or higher; foreign; semTools, qgraph; semPlot)

Mplus 8 or higher (demo version)

Hardware Requirements

Computer lab, no other specific requirements


Arbuckle, J. L., 2016: IBM SPSS Amos 24 User’s Guide. Armonk, NY: IBM.

Bollen, K. A., 1989: Structural equations with latent variables. New York: John Wiley and Sons.

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

Brown, T. A., 2015: Confirmatory Factor Analysis for Applied Research (2nd edition). New York/London: Guilford.

* Byrne, B. M., 2016: Structural Equation Modeling with AMOS. Basic Concepts, Applications and Programming (3rd edition). New York/London: Routledge.

* Byrne, B. M., 2013: Structural Equation Modeling with Mplus. Basic Concepts, Applications and Programming. New York/London: Routledge.

* Gana, K./Broc, G., 2019: Structural Equation Modeling with lavaan. London: Wiley

* Kline, R. B., 2016: Principles and Practice of Structural Equation Modeling (4th edition). New York/London: Guilford.

Kline, R. B., 2011: Principles and Practice of Structural Equation Modelling (3rd edition). New York/London: Guilford.

Maruyama, G. M., 1998: Basics of structural equation modelling. Thousand Oaks: SAGE Publications, Inc.

Ping, R.A., 1996: Latent Variable Interaction and Quadratic Effect Estimation: A Two-Step Technique Using Structural Equation Analysis. Psychological Bulletin 119 (1): 166-175.

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

Schumacker, R. E./Lomax, R. G., 2016: A beginner`s guide to structural equation modeling (4th edition). Mahwah: Lawrence Erlbaum Associates.

Recommended Courses to Cover Before this One

Winter School

Structural Equation Modelling (SEM) with R

Summer School

Introduction to Inferential Statistics: What you need to know before you take regression

Multiple Regression Analysis: Estimation, Diagnostics, and Modelling

Advanced Topics in Applied Regression

Recommended Courses to Cover After this One

Winter School

Structural Equation Modelling (SEM) with R

Summer School

Multi-Level Structural Equation Modelling

Advanced Structural Equation Modelling