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Structural Equation Modelling (SEM) with R

Julia Koltai

Eötvös Loránd University

Julia Koltai is an assistant professor at the Faculty of Social Sciences, Eötvös Loránd University. She is also a research fellow at the Centre for Social Sciences, Hungarian Academy of Sciences. She gained her PhD in sociology in 2013.

Julia has led several domestic research programs and has taken part in international research projects and groups, including EU FP6-funded programs.

Her main scientific focus is on statistics and social research methodology, so her research has ranged widely, from minority research through political participation to social justice and integration.

In recent years, Julia's interest has turned to computational social science, especially network analysis and big data processing.


Course Dates and Times

Monday 25 February – Friday 1 March, 09:00 – 12:30
15 hours over 5 days

Prerequisite Knowledge

Participants should understand basic principles of regression analysis and the meaning of regression results. A basic understanding of principal component analysis (explorative factor analysis) would be helpful. Participants should have some familiarity with software R to manage data.

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, contact the instructor before registering.

Short Outline

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

It answers the question, why is it more beneficial to use SEM, compared to classical path models. It is shown, how the theoretical latent constructs (e.g. social and political attitudes, and values) can be measured and explained with their relationships with other variables. The course highlights the theoretically and empirically important aspects of model comparison between different groups (such as countries or different years in a longitudinal survey).

Participants have to bring their own laptops: both PC/Windows and Mac are OK with R Studio – with the later mentioned software version and packages. (Participants will need to have user privileges that allow them to install R and R packages. If they have limited access – because for example it is a work laptop and unsure – consult with IT tech person first.)

Tasks for ECTS Credits

  • Participants attending the course: 2 credits (pass/fail grade) The workload for the calculation of ECTS credits is based on the assumption that students attend classes and carry out the necessary reading and/or other work prior to, and after, classes.
  • Participants attending the course and completing one task (see below): 3 credits (to be graded)
  • Participants attending the course, and completing two tasks (see below): 4 credits (to be graded)

2 credits (pass/fail grade) Attend at least 90% of course hours, participate fully in in-class activities, and carry out the necessary reading and/or other work prior to, and after, class.

3 credits (to be graded) As above, plus complete one task (tbc).

4 credits (to be graded) As above, plus complete two tasks (tbc).

Long Course Outline

Structural Equation Modelling (SEM) is a powerful tool to analyze latent variable models that are common in social sciences, e.g. the analysis of social and political attitudes or social values. SEM combines factor analysis and path analysis by simultaneously estimating relations between latent constructs and/or manifest variables, and also relations of latent constructs and its corresponding manifest indicators. Additionally, SEM 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. Additionally, SEM is capable to compare these models between different groups, like countries or waves of a longitudinal study, or also social groups.

The course introduces to theory and practice of SEM on a general level. During the course, R software will be used.

Basic modelling techniques of SEM are explained and applied by exercises using free access social science data. Additionally, participants have got the possibility to use their own data for analyses. Daily assignments allow the application and transfer of SEM methodology to own research interests.

On the first day we go through the statistical and methodological basics of SEM, such as regression analysis and classical path model analysis. We show the advantages of SEM and present its fitting principles. Basic (visual and statistical) notations and statistical tests and indices will be mentioned. On the second day, we focus on the first step of building a SEM model, namely the usage of confirmatory factor analysis (CFA) for the creation of latent constructs. Comparison with other factor analysis methods will be presented. We go through different model-building (parametrisation) and model improving techniques as well. The practical implementation of this knowledge will be possible on the lab session. On the third day the latent variable model will be expanded with other, explanatory variables to get a more complex and interpretable model. These models are better for answering a scientific research question as they give more space for explanation. There will be possibility again for the application of these models, with emphasis on the interpretation and practical questions. On the fourth day, the class will be about multiple group comparison, which is – taking the different levels of testing into account – one of the most useful part of SEM. The class starts with the theoretical problems of multi-group comparison and connects these problems with SEM tools, that can help to decide the depth of the comparison. A step-by-step guide will be provided for the participant to be able to proceed such analysis. In the lab session, technical advises will be given about the measurement and realization of these models, especially about the interpretation of the different results. The last day is to summarize the knowledge studied during the week, with the help of a concrete example, where all the techniques will be applied. After going through a complex example, the consequences will be generalised, and other suggestions will be drawn. Finally, some practices will be presented for publication of papers, which include SEM methods.


Day Topic Details
1 Introduction to latent variable modeling and Confirmatory Factor Analysis (CFA) – Different types of SEMs – Fundamentals of the lavaan syntax – Specification of measurement models based on covariance matrix and raw data – Model identification, calculation of the observed and estimated parameters – Interpretation of the lavaan output – Draw SEM diagrams
2 Evaluating model fit, dealing with missingness, using different estimators and estimating reliability – Evaluating model fit values (χ², df, CFI, RMSEA, SRMR), their calculation and limitations – Types of missingness (MAR, MCAR, etc.) – Estimators for categorical/dichotomous and continuous variables – Strengths and weaknesses of parceling – Reliability coefficients (McDonald’s ω, Cronbach’s α)
3 Improving models and advanced modeling techniques – Equivalent and nested models – Specification of different models, among others: • higher-order models • correlated trait correlated uniqueness model • correlated trait correlated method models • nested factor models – Structural regression models – Models with covariates (MIMIC)
4 Testing measurement invariance with Multi-Group Confirmatory Factor Analysis (MGCFA) – Logic of measurement invariance (MI) testing – Common MI testing procedure across groups (configural, metric, scalar, and strict MI) – Partial measurement invariance – MI testing with dichotomous/ordinal data
5 Latent-State-Trait-Analysis and Latent-Change-Models – Autoregressive models – Cross-lagged panel analysis – Latent state analysis – Latent state trait analysis – Latent change models – Latent change curve models
Day Readings
1 Raykov, T. & Marcoulides, G. A. (2006). A first course into Structural Equation Modeling. Lawrence Erlbaum Associates: Mahwah, New Jersey. (Chapter 1 and 4) Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48, 1–36. retrieved from
2 Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6, 1–55. Mueller, R. O. (1997). Structural equation modeling: Back to basics. Structural Equation Modeling: A Multidisciplinary Journal, 4, 353–369. Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7, 147–177. doi:10.1037//1082-989X.7.2.147 Non-obligatory reading: Whittaker, T. A. (2012). Using the modification index and standardized expected parameter change for model modification. The Journal of Experimental Education, 80, 26–44. doi:10.1080/00220973.2010.531299

Brunner, M., Nagy, G., & Wilhelm, O. (2012). A tutorial on hierarchically structured constructs. Journal of Personality, 80, 796–846. doi:10.1111/j.1467-6494.2011.00749.x Schroeders, U., & Wilhelm, O. (2010). Testing reasoning ability with handheld computers, notebooks, and paper and pencil. European Journal of Psychological Assessment, 26, 284–292. doi:10.1027/1015-5759/a000038 Non-obligatory reading: Eid, M., Lischetzke, T., & Nussbeck, F. W. (2006). Structural equation models for multitrait-multimethod data. In M. Eid & E. Diener (Eds.), Handbook of multimethod measurement in psychology (pp. 283–299). Washington, DC: American Psychological Association. Schulze, R. (2005). Modeling Structures of Intelligence. In O. Wilhelm & R. W. Engle (Eds.), Handbook of understanding and measuring intelligence (pp. 241–263). Thousand Oaks, CA: Sage Publications.

4 Non-obligatory reading: Vandenberg, Robert J. & Lance, Charles E. (2000). A Review and Synthesis of the Measurement Invariance Literature: Suggestions, Practices, and Recommendations for Organizational Research. Organizational Research Methods, 3, 4–70.
5 Geiser, C., Crayen, C. & Enders, C. (2014). Advanced Multivariate Data Analysis with Mplus. Springer: Heidelberg. Non-obligatory reading: Little, T. D., Preacher, K. J., Selig, J. P., & Card, N. A. (2007). New developments in latent variable panel analyses of longitudinal data. International Journal of Behavioral Development, 31, 357–365. Preacher, K. J. (2010). Latent growth curve models. In G. R. Hancock & R. O. Mueller (Eds.), The reviewer's guide to quantitative methods in the social sciences (pp. 185–198). London: Routledge.

Software Requirements

R version 3.5.2 or higher. With RStudio Desktop version 1.1.463 or higher. With R packages: foreign version 08-71 or higher; lavaan version 0.6-3 or higher; sem version 3.1-9 or higher; semTools 0.5-1 or higher, qgraph 1.5 or higher; semPlot version 1.1 or higher; ggplot2 version 3.1.09000 or higher; survey version 3.35 or higher.


Hardware Requirements

Participants have to bring their own laptops: both PC/Windows and Mac are OK with R Studio – with the abovementioned software version and packages. Participants will need to have user privileges that allow them to install R and R packages. If they have limited access – because for example it is a work laptop and unsure – consult with IT tech person first.

Recommended Courses to Cover Before this One

<p><strong>Summer School</strong></p> <p>Introduction to Inferential Statistics: What you need to know before you take regression<br /> Multiple Regression Analysis: Estimation, Diagnostics, and Modelling</p> <p><strong>Summer School</strong></p> <p>Regression Refresher (before you take a more advanced stats course)<br /> Linear Regression with R/Stata: Estimation, Interpretation and Presentation</p> <p>&nbsp;</p>

Recommended Courses to Cover After this One

<p><strong>Summer School</strong></p> <p>Multi-Level Structural Equation Modelling</p>

Additional Information


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.