Structural equation modeling (SEM)

Structural equation modeling (SEM) is an advanced statistical analysis technique that is used by scientists in various fields. SEM diagrams look much like concept maps and allow readers to ascertain the essence of a study in a visual format. A single SEM diagram can often convey more information than multiple tables of results from linear regression studies. SEM provided a breakthrough in theory testing by enabling researchers to examine the effects of complex constellations of variables on outcomes thoroughly and efficiently. Especially valuable in SEM is the ability to test how pivotal variables, called mediators, explain the effects of more distal variables on outcomes.

Overview

Prior to SEM’s rise in popularity, researchers and statisticians relied more heavily on various forms of linear regression to predict outcomes. Linear regression is very valuable and still popular, but it does not as readily allow for testing the complex interrelationships among variables. Human brains are capable of both linear reasoning and parallel processing; both are valuable, but parallel processing is often necessary when analyzing rather complex sets of information. In studies, SEM figures resemble concept maps and often include the actual results of the study, making it easier to remember the researchers’ concepts and findings, especially for a person who favors visual-spatial thinking.

Latent variables are important in SEM. Represented by circles in SEM diagrams, they are composed of two or more directly measured variables, which are known as observed variables and represented in diagrams by squares. Latent variables are not directly measured by researchers; rather, they are statistically constructed composites of the theoretically related observed variables. For instance, a researcher could use four observed variables averaged across a neighborhood, such as levels of exercise, green space, positive social relationships, and safety, to compose a latent variable indicating the well-being of the neighborhood. Another scientist might use five different measures of how happy respondents feel in different aspects of their lives, each observed variable, to form the latent variable happiness.

Another key concept in SEM is the testing of mediators. Mediators are variables that exert their influence on an outcome on behalf of a variable that is otherwise not as closely connected with the outcome. For instance, parents’ expectations that their young children will eventually graduate from college and earn an advanced degree promote various aspects of students’ success during adolescence, but this effect is mediated by other important variables, such as children’s expectations. Researchers who study parent expectations in a linear fashion may underestimate the effect of those expectations if they fail to account for important mediators.

Advancements in SEM continued to focus on expanding its capabilities to handle complex multilevel and longitudinal data structures with robust estimation methods. Developments like dynamic structural equation models (DSEM) can handle non-independent observations and missing data, offering more flexibility and applicability. SEM was used to study social phenomena, species evolution, and market trends and to model disease risk. In the 2020s, it was also being used to study people's use of artificial intelligence (AI), like in medical and educational settings. SEM software like IBM SPSS Amos, JMP Pro 18, and Stata SEM Builder continued evolving as well. 

Bibliography

"A Comprehensive Guide to Structural Equation Modeling." Statistics Solutions, www.statisticssolutions.com/free-resources/directory-of-statistical-analyses/structural-equation-modeling. Accessed 19 Mar. 2026.

Davison, Mark L., et al. “Modeling Configural Patterns in Latent Variable Profiles: Association with an Endogenous Variable.” Structural Equation Modeling: A Multidisciplinary Journal, vol. 21, no. 1, 2014, pp. 81–93, doi:10.1080/10705511.2014.859507. Accessed 19 Mar. 2026.

Falebita, Oluwanife Segun, and Petrus Jacobus Kok. "Artificial Intelligence Tools Usage: A Structural Equation Modeling of Undergraduates’ Technological Readiness, Self-Efficacy and Attitudes." Journal for STEM Education Research, vol. 8, 2025, pp. 257–82, DOI:10.1007/s41979-024-00132-1. Accessed 19 Mar. 2026.

Hoyle, Rick H. Handbook of Structural Equation Modeling. 2nd ed., Guilford Publications, 2023.

Hu, Li-tze, and Peter M. Bentler. “Cutoff Criteria for Fit Indexes in Covariance Structure Analysis: Conventional Criteria versus New Alternatives.” Structural Equation Modeling, vol. 6, no. 1, 1999, pp. 1–55.

Kenny, David A., et al. Dyadic Data Analysis. Guilford, 2006.

Kline, Rex B. Principles and Practice of Structural Equation Modeling. 5th ed., Guilford, 2023.

Loehlin, John C., and A. Alexander Beaujean. Latent Variable Models: An Introduction to Factor, Path, and Structural Equation Analysis. 5th ed., Taylor & Francis Group, 2017.

Shin, Tacksoo, et al. “Effects of Missing Data Methods in Structural Equation Modeling with Nonnormal Longitudinal Data.” Structural Equation Modeling: A Multidisciplinary Journal, vol. 16, no. 1, 2009, pp. 70–98.