Introduction to Structural Equation Modeling (SEM)

About

Workshop Contents and Objectives

The objective of this course is to show how structural equation modeling can be used to develop and/or test both measurement models (scales) and causal theories between latent variables with survey data. In the first part we deal with building scales by employing confirmatory factor analysis, simultaneous factor analysis, bifactor models, multiple group factor analysis and higher order factor analysis as well as measurement invariance over groups and countries. When discussing full structural equation modeling, we will treat formative and reflective indicators, mediation, indirect effects, moderation and multiple group structural equation modeling. A further important aim is to familiarize participants with the AMOS program. The program will be run by graphical input via path diagrams (AMOS Graphics). A special focus will be given to the analysis of comparative data across groups. This includes how to test for measurement invariance using multiple group confirmatory factor analysis.

Participants are strongly encouraged to bring their own data, prepare in advance the raw data or correlations and standard deviations according to the specifications necessary for AMOS or R-lavaan, and apply the new procedures besides the prepared examples of the instructors in the practical sessions. Everyone will be able to receive consultation and have the opportunity to present own first results on the last day to receive feedback and recommendations for further analyses. While Amos would be used for the practical exercises, the relevant syntax for R-lavaan would also be provided.

Workshop design

A combination of either live lectures or recorded video lectures, theoretical exercises as well as applied exercises with the program Amos, group work where applicable, and individual or group work on own models with consultation and a presentation on the last day of the course.

Deatiled lecture plan (daily schedule)

Day 1.
Basic ideas of measurement models

Day 2.
Confirmatory factor analysis (CFA)

Day 3.
Variants of Confirmatory Factor Analysis Models (Bifactor, MTMM, Higher Order), Multiple Group Confirmatory Factor Analysis (MGCFA) and introduction to Structural Equation Modeling (SEM)

Day 4.
SEM

Day 5.
Presentations of participants and summary, open questions

See course outline below for details.

COURSE OUTLINE

The course will show how a causal theory can be represented by a path diagram and translated into a confirmatory factor and/or a full structural equation model and how the model can be estimated and tested with the AMOS computer program. In the first part we will deal with measurement models relating single or multiple indicators to latent variables. Furthermore, different specifications of measurement models are tested via confirmatory factor analysis as a special case of a structural equation model. The second part comprises both the structural and the measurement model. Topics include treatment of cross-cultural data with multiple-group modeling, Mimic models, moderation and mediation, and missing values. Special attention is given to the process of model modification. We warmly recommend participants to bring their own data with them. Time will be dedicated for consultation on Thursday, and participants will have the opportunity to present their models on the last day of the course to get feedback for 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 the AMOS manual, 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: AMOS 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: Arbuckle 2017 Introduction and chapters 22, 26 and 27, Examples 1, 3; Byrne 2010 (ToolBox) and chapter 4; 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).

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; Arbuckle 2017 Examples 10 and 12.

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: Arbuckle 2017 Examples 15, 24, Appendix E, F and G; 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); Arbuckle 2017 chapter 5; 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); Arbuckle 2017 Example 7; McKinnon et al. 2007; Davidov et. al. 2008; Kline(2023, parts II - IV); Schmidt & Herrmann 2011, Steinmetz et al. 2011.Additional Reading: Berry 1984; Arbuckle 2009 Example 25; Heyder & Schmidt 2002 (23-24); Yang-Wallentin et. al. 2006.

Day 5.
Participants’ presentations.

Essential Reading: Arbuckle 2009 Example 17 and 18.

**The Summer School cannot grant credits. We only deliver a Certificate of Participation, i.e. we certify your attendance.**

If you consider using Summer School workshops to obtain credits (ECTS), you will have to investigate at your home institution (contact the person/institute responsible for your degree) to find out whether they recognise the Summer School, how many credits can be earned from a workshop/course with roughly 35 hours of teaching, no graded work, and no exams.

Make sure to investigate this matter before registering if this is important to you

Course leader

Eldad Davidov is professor in methodology at the Department of Sociology and Social Psychology at the University of Cologne. Peter Schmidt is professor emeritus of social science methodology at the University of Giessen, and member of its International Centre for Development and Environmental Research (ZEU)

Target group

primarily graduate researchers, PhD researchers, early career researchers

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.

Fee info