A tutorial for understanding SEM using R: Where do all the numbers come from?

Area of Science:

• Statistics
• Quantitative Psychology
• Data Science

Background:

• Structural Equation Modeling (SEM) is perceived as complex.
• Understanding SEM's underlying computations in software output is challenging.
• Open-source SEM tools in R exist but their source code can be overwhelming.

Purpose of the Study:

• To provide an accessible introduction to the basic computations behind standard SEM analyses.
• To clarify how SEM software output numbers are computed.
• To enhance reader understanding of SEM's internal workings.

Main Methods:

• Manual reproduction of key SEM results using simple R scripts.
• Utilizing two well-known example datasets for demonstration.
• Focusing on clarity and conceptual understanding over computational efficiency.

Main Results:

• Demonstrated manual computation of parameter estimates.
• Showcased reproduction of standard errors.
• Illustrated the calculation of SEM fit measures.

Conclusions:

• Readers can gain a better grasp of SEM "under the hood" through manual computation.
• This tutorial facilitates applying SEM computational concepts in independent research.
• Demystifies SEM calculations, making the method more approachable for researchers.