Master
2019/2020

## Introduction to Structural Equation Modeling

Type:
Compulsory course (Comparative Social Research)

Area of studies:
Sociology

Delivered by:
Department of Sociology

When:
1 year, 4 module

Mode of studies:
offline

Instructors:
Boris Sokolov

Master’s programme:
Comparative Soсial Research

Language:
English

ECTS credits:
4

### Course Syllabus

#### Abstract

The course is intended to give an introduction to the foundational concepts and basic computational techniques of structural equation modeling (SEM) and their implementation in a popular SEM software tool, R package lavaan. The topics covered by the course are exploratory and confirmatory factor analysis (E/CFA), measurement invariance, path models, and structural equation models. In addition, practical issues of estimation (including Bayesian estimation), visualization and presentation of various types of SEM models are discussed. To succeed in this course, students are assumed to have basic knowledge of statistics and be familiar with several conventional statistical methods, most importantly regression anal-ysis. In addition, for practical exercises we will use R programming environment, so an-other major prerequisite is a basic knowledge of R.

#### Learning Objectives

- The main goals of this course are (a) to help students learn the foundational concepts of structural equation modelling, (b) to explain them the key principles of model building, assessment, comparison, and modification in SEM, and (3) to illustrate how they can use a powerful statistical software, R, to utilize these concepts and principles in real-data applications of SEM.

#### Expected Learning Outcomes

- Understand foundational concepts of confirmatory factor analysis (CFA) and structural equation modeling (SEM)
- Understand basic assumptions of CFA and SEM models
- Understand and apply in practice basic principles of model building, model evaluation and model modification in CFA and SEM
- Build, estimate, assess, compare and modify confirmatory factor an/or structural models using R packages lavaan and semTools
- Visualize various types of measurement and structural models using R package semPlot
- Understand the concept of measurement invariance and apply different approaches to measurement invariance testing
- Conduct multigroup confirmatory factor analysis (MGCFA) and test for measurement in-variance using R packages lavaan and semTools
- Apply different approaches to theory testing in SEM
- Understand the concepts of moderation and mediation in SEM
- Conduct mediation analysis in lavaan

#### Course Contents

- IntroductionCourse overview. The concept of latent variable. The concept of construct. Reflective vs. Forma-tive measurement. General factor model. Principal component analysis (PCA). Kaiser’s rule. Scree plots. Bi-plots. Exploratory factor analysis (EFA). Confirmatory factor analysis (CFA). Differences between CFA and EFA. R implementation of PCA and EFA.
- Confirmatory Factor Analysis – 1: Basics of CFAConfirmatory factor model: assumptions, key model parameters, notation. Maximum likelihood estimation of CFA-models. Observed vs. predicted VCOV matrices. Model identification. Not identified, just identified and over identified CFA models. Various types of parameter con-straints used for model identification. Standardization. Model fit and key fit indices. Estimation of CFA models using the R package lavaan. Visualization of CFA models using semPlot
- Confirmatory Factor Analysis – 2: Model Correction and Validity Assessment.Basic principles of CFA model improvement. Modification indices (MI). Expected parameter change (EPC). Standardized residuals. Model comparison: Fit indices and chi-square difference test. Measurement validity. Different types of validity: content validity and construct validity (convergent and discriminant). Reliability: Cronbach’s alpha and other measures. Handling miss-ing data: listwise/pairwise deletion and full information maximum likelihood.
- Confirmatory Factor Analysis – 3: Non-normal and categorical data.Problems with non-normal and categorical data. Which data are (reasonably) non-normal and which are categorical. Robust versions of the maximum likelihood estimator. CFA model for cat-egorical data: key parameters and notation. Weighted least squares estimation. lavaan implemen-tation. Interpretation, visualization, assessment, modification, and comparison of categorical CFA models.
- Multi-Group CFA and Measurement InvarianceMulti-group CFA (MGCFA). The concept of measurement invariance (equivalence). Types of invariance: configural, metric and scalar. Invariance testing with lavaan. Using semTools for au-tomated invariance testing in R. Multi-group categorical CFA (MGCCFA). Required parameter constraints for model identification in MGCCFA. Delta vs. Theta parameterization. MGCCFA implementation in lavaan. What to do when measurement invariance is lacking?
- Structural ModelsBasic concepts of structural modelling. Measurement model vs. structural model. Path models. Exogenous and endogenous variables. Recursive and non-recursive models. Identification of structural models. Multiple-indicator multiple-cause (MIMIC) models. Structural regression mod-els. lavaan implementation. Interpretation, visualization, assessment, modification, and compari-son of path models and structural models.
- Mediation analysisSubstantive importance of mechanism modeling. The concept of mediation. Full and partial me-diation. Indirect and total effects and their computation in lavaan. Baron-Kenny approach to mediation. Uncertainty estimation: Sobel’s test and bootstrap. Interpretation, assessment, and comparison of models with mediation. Other types of third variables: moderation and confound-ing. Equivalent models.

#### Assessment Elements

- Home assignment 1Take-home written assignment, in which you should analyze a real data set using FA/SEM methods discussed in Lectures 1-4. All assignments have to be submitted by email to the course instructor by 23:59, May 22nd, 2020.
- Class activity
- Final examTake-home written assignment, in which you should analyze a real data set using FA/SEM methods. Specifically, you should first use exploratory methods to develop a meaning-ful, theoretically interpretable factor model. Then you apply the confirmatory approach to assess your model’s quality and modify it, if necessary. Finally, you are asked to test whether your latent variable(s) is non-trivially related to a set of external variables. All assignments have to be submitted by email to the course instructor by 23:59, June 18th, 2020. Notice that in the final paper you may either (1) analyze a data set provided by the in-structor or (2) analyze your own data. Re-gardless of your specific data preference, the same grading principles and criteria (see be-low) will be applied to the assessment of your final submission in both cases. The deadline for submission of your exam paper is noon of June 13th, 2020. Then all papers will be evaluated by the instructor and preliminary grades will be announced. Then those course participants who disagree with their preliminary grades will have an opportunity to defend their project papers (by publicly presenting them in class). Presentations must be given using Power-Point or LaTeX software.
- Home assignment 2Take-home written assignment, in which you should analyze a real data set using FA/SEM methods discussed in Lectures 5-7. All assignments have to be submitted by email to the course instructor by 15:10, June 9th, 2020.

#### Interim Assessment

- Interim assessment (4 module)0.15 * Class activity + 0.35 * Final exam + 0.25 * Home assignment 1 + 0.25 * Home assignment 2

#### Bibliography

#### Recommended Core Bibliography

- Brown, T. A. (2015). Confirmatory Factor Analysis for Applied Research, Second Edition (Vol. Second edition). New York: The Guilford Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=831411
- Kline, R. B. (2016). Principles and Practice of Structural Equation Modeling, Fourth Edition (Vol. Fourth edition). New York: The Guilford Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1078917

#### Recommended Additional Bibliography

- Westland, J. C. (2019). Structural Equation Models : From Paths to Networks (Vol. 2nd ed). Cham, Switzerland: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2097529