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Structural Equation Modeling (SEM) with R

Ulrich Schröders

University of Kassel


Course Dates and Times

Monday 5 to Friday 9 March 2018
15 hours over 5 days

Prerequisite Knowledge

Prospective participants should possess a solid knowledge of basic statistical concepts (e.g., variance, covariance, correlation) and of manifest regression analyses (e.g., prediction, standard error). They should also be familiar with the terms often used in test theory (e.g., items, scale, reliability, validity). With regard to software, potential participants should have worked with R on a productive level. More specifically, participants should be able to read in data from different sources, to select and to reference specific variables and observations within a given data set, and to calculate basic descriptive statistics (mean, correlation, etc.). They should be familiar with RStudio or any another R programming environment. In the course a combination of Notepad++ and NppToR will be used to write and execute R syntax; but previous experience with this simple software solution is not necessary.

Short Outline

This course deals with intermediate and advanced aspects of Structural Equation Modeling (SEM), a method that is popular in psychology, educational research, and the social sciences. The course begins with a comprehensive introduction to the theoretical aspects of SEM and its terminology. Among others, issues of model identification, handling of missing data and the appropriate use of different estimators are discussed and trained in practical exercises which are an essential part of each session. Further topics include aspects of reliability, model fit evaluation, improving model fit, testing of measurement invariance, and longitudinal data modeling. The overall aim of the course is to acquire a deeper understanding of latent variable modeling and to develop skills in order to estimate, interpret, and tweak SEMs. All analyses will be conducted with the R package lavaan.

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)

Long Course Outline

This course deals with intermediate and advanced aspects of Structural Equation Modeling (SEM), a method that is becoming more and more popular in the behavioral and social sciences. The course comprises five three-hour sessions; the time for each session is divided equally into a theoretical and a practical part. In this context, various examples from educational research, psychology, and the social sciences are discussed. The course starts with a conceptual overview of the different classes of structural equation models and introduces the basic terminology that is used throughout the course. Furthermore, key concepts such as model identification or the distinction between covariance and mean structure are covered. After this overview, the participants are introduced to the fundamentals, the logic, and the syntax of the R package lavaan that is subsequently used for all structural equation modeling.

Participants learn to specify Confirmatory Factor Analyses (CFA) and interpret the lavaan output. In comparison to other latent variable approaches such as IRT, SEM has the advantage of providing good omnibus tests for model fit evaluation. Accordingly, participants calculate different fit statistics (e.g., CFI, RMSEA, SRMR), learn their adequate use and their limitations. As empirical research is often accompanied by some limitations of the data, most prominently, missingness or skewed distributions of variables, the course training also includes handling of missing data, usage of different estimators (e.g., for categorical/dichotomous and continuous variables), and correcting of parameter estimation for nested data structure. Moreover, strengths and weaknesses of item parceling are also addressed.

In many cases an initial, theory-driven CFA model will not fit the data perfectly. We will pay close attention to sources of model misspecification and ways how to improve model fit by data-drive adjustments. On the other hand, we will address some basic philosophical and statistical issues that are often neglected, but have to be taken into account before sound SEM analyses are conducted. Participants will also become acquainted with different modeling approaches (higher-order models, nested factor models, CTCM, CTCU, etc.) and understand their statistical and interpretational differences. As SEM is a powerful method to test competing theories, we will also discuss how to conduct model comparisons of nested and non-nested models. Furthermore, both structural regression models which postulate regressions between latent variables and models that include manifest covariates (MIMIC approach) are examined.

Testing for measurement invariance is a necessary prerequisite to making valid statements about group differences. For instance, in order to ascertain that boys outperform girls in mathematics it is necessary to demonstrate that the assumptions of strong measurement invariance holds (i.e., that we are measuring the same construct in both groups identically). A common, straightforward procedure of testing for measurement invariance is Multi-Group Confirmatory Factor Analysis (MGCFA). Moreover, we extend the procedure to ordinal data and also discuss the concept of partial measurement invariance.

Because of its flexibility SEM is often employed to analyze longitudinal data, besides cross-sectional data. In the last part of the course, we expand our exercises to longitudinal data. One class of models deals with modeling variability of scores around time-stable traits; the other class of models we will get to know is concerned with change in latent variables over time (i.e., latent growth curve modeling). The focus is on (latent) cross-lagged panel analysis and latent change score models. In the last session there will also be time to answer further questions concerning topics discussed in previous sessions or specific issues of the participants.

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

1) most recent version of R (e.g., 3.2.0) 2) most recent version of the R package lavaan 3) Additionally, the R packages psych, foreign, MBESS, semTools, semPlot (via CRAN) 4) Rstudio OR (Notepad++ (e.g., v6.6.3, see & NppToR (see

Hardware Requirements


Recommended Courses to Cover Before this One

<p>Introduction to R</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.