Stuctural Equation Modeling

Workshop AgroStat 2024

Introduction

• This AGROSTAT2024 pre-conference workshop will held on 3 September 2024 in Bragança. All its material is available at https://galharret.github.io/SEM_AGROSTAT2024/

What is a structural equation model?

• Structural equation modeling generalizes linear regression models.

• These models have been introduced into social and psychological studies in the 70’s.

• SEM can be used to produce regression models between latent variables.

The two approaches

• Covariance Analysis: Jöreskog (1970)

• Partial Least Square (PLS): Wold (1980)

\(\leadsto\) In this workshop we will focus on the covariance analysis with the most theoritical and mathematical background.

Jöreskog

Wold

Some reference books

Bollen (1989)

Kline (2023)

Chen and Yung (2024)

Pugesek et al (2007)

Contents of the workshop

• SEM without a measurement model: Path modeling

• SEM with a measurement model: Factor Analysis and structural relation.

SEM Terminology and Notations

In SEM, two categories of variables are involved:

• Exogenous variable (denoted by \(\xi\)) who are deterministic. These values are independent from the values of the other variables of the model. Normal regression models assume that the predictors are exogenous.

• Endogenous variable (denoted by \(\eta\)) who are stochastic and who are correlated with the error of the model. These values are depending of the values of other factors involved in the model.

In the first example \(X_1\) is exogenous and \(X_2,X_3\) are endogenous.

Software

Lavaan is a the most popular package on R for latent variable modelling.

• The official reference of lavaan: Rosseel (2012)

• Its website : lavaan.org

• For installing lavaan and SemTools:

install.packages(c("lavaan","semTools"), dependencies = TRUE)

Bollen, Kenneth A. 1989. Structural Equations with Latent Variables. 1st ed. Wiley. https://doi.org/10.1002/9781118619179.

Chen, Ding-Geng, and Yiu-Fai Yung. 2024. Structural Equation Modeling Using r/SAS: A Step-by-Step Approach with Real Data Analysis. First edition. Boca Raton: CRC Press.

Jöreskog, K. G. 1970. “A General Method for Analysis of Covariance Structures.” Biometrika 57 (2): 239–51. https://doi.org/10.1093/biomet/57.2.239.

Kline, Rex B. 2023. Principles and Practice of Structural Equation Modeling. Fifth edition. Methodology in the Social Sciences. New York: The Guilford Press.

Rosseel, Yves. 2012. “Lavaan : An R Package for Structural Equation Modeling.” Journal of Statistical Software 48 (2). https://doi.org/10.18637/jss.v048.i02.

Wold, Herman. 1980. “Model Construction and Evaluation When Theoretical Knowledge Is Scarce.” In, 47–74. National Bureau of Economic Research, Inc. https://EconPapers.repec.org/RePEc:nbr:nberch:11693.