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

Structural equation modeling (SEM) is often seen as a complex and difficult method, especially for those who want to understand how the numbers in SEM software output are actually computed. Although many open‐source SEM tools are now available—especially in the R programming environment—looking into their source code to understand the underlying calculations can still be overwhelming. This tutorial aims to provide a clear and accessible introduction to the basic computations behind standard SEM analyses. Using two well‐known example datasets, we show how to manually reproduce key results such as parameter estimates, standard errors, and fit measures using simple R scripts. The focus is on clarity and understanding rather than speed or efficiency. We hope that by following this tutorial, readers will gain a better grasp of how SEM works “under the hood,” and be able to apply similar ideas in their own research.