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 thoroughly and efficiently examine the effects of complex constellations of variables on outcomes. Especially valuable in SEM is the ability to test how pivotal variables, called mediators, explain the effects of more distal variables on outcomes.


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 variables, 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. Likewise, SEM may help researchers in various fields capture a clearer picture of how a particular variable has an effect on outcomes.

—John Mark Froiland, PhD

Davison, Mark L., Yu-Feng Chang, and Ernest C. Davenport. “Modeling Configural Patterns in Latent Variable Profiles: Association with an Endogenous Variable.” Structural Equation Modeling 21.1 (2014): 81–93. Print.

Hoyle, Rick H., ed. Handbook of Structural Equation Modeling. New York: Guilford, 2012. Print.

Hu, Li-tze, and Peter M. Bentler. “Cutoff Criteria for Fit Indexes in Covariance Structure Analysis: Conventional Criteria versus New Alternatives.” Structural Equation Modeling 6.1 (1999): 1–55. Print.

Kenny, David A., Deborah A. Kashy, and William L. Cook. Dyadic Data Analysis. New York: Guilford, 2006. Print.

Kline, Rex B. Principles and Practice of Structural Equation Modeling. 3rd ed. New York: Guilford, 2011. Print.

Loehlin, John C. Latent Variable Models: An Introduction to Factor, Path, and Structural Equation Analysis. 4th ed. New York: Routledge, 2011. Print.

Shin, Tacksoo, Mark L. Davison, and Jeffrey D. Long. “Effects of Missing Data Methods in Structural Equation Modeling with Nonnormal Longitudinal Data.” Structural Equation Modeling 16.1 (2009): 70–98. Print.