How does SEM differ from ordinary regression?

It allows multiple equations, latent variables measured by several indicators with explicit measurement error, and the simultaneous estimation of an entire system rather than a single response on predictors.

Can SEM prove causation?

No. It tests whether a specified causal structure is consistent with the data, but causal interpretation rests on assumptions that observational data alone cannot verify.

Structural Equation Modeling

Structural equation modeling fits systems of equations relating latent constructs to one another and to their observed indicators by matching the model-implied and observed covariance structures.

Definition

Structural equation modeling is a multivariate method that estimates the parameters of a hypothesized system linking latent and observed variables by fitting the covariance structure it implies to the sample covariance matrix.

Scope

This topic covers the combination of a confirmatory-factor measurement model with a structural model of regression-like relations among latent variables, path diagrams, model identification, estimation by minimizing a discrepancy between observed and model-implied covariance matrices, and assessment of fit through global and local indices.

Core questions

How can a theory expressed as relations among latent constructs be tested against data?
How are measurement and structural parts of a model specified together?
When is a structural equation model identified?
How is the fit of the model evaluated?

Key theories

Covariance structure fitting: The model implies a covariance matrix as a function of its parameters, and estimation chooses parameter values minimizing a discrepancy between this implied matrix and the observed sample covariance matrix.
Measurement plus structural model: A confirmatory factor measurement model links latent variables to indicators while a structural model specifies directed relations among the latent variables, so that measurement error is modeled explicitly and separated from structural relations.

Clinical relevance

Structural equation modeling is widely used in the social, behavioral, and health sciences to test theoretical models involving constructs measured with error, such as mediation and pathways among latent variables.

History

Structural equation modeling brought together Wright's path analysis from genetics and the confirmatory factor tradition from psychometrics, formalized in the 1970s through covariance structure models and software, and has since become a standard tool across the social sciences.

Debates

Fit indices and model acceptance: Reliance on cutoff values for global fit indices to accept or reject models is contested, since such thresholds are heuristics that can mislead about a model's adequacy.

Key figures

Karl Joreskog
Kenneth Bollen
Sewall Wright

Seminal works

bollen1989
kline2016
bartholomew2011

Frequently asked questions

How does SEM differ from ordinary regression?: It allows multiple equations, latent variables measured by several indicators with explicit measurement error, and the simultaneous estimation of an entire system rather than a single response on predictors.
Can SEM prove causation?: No. It tests whether a specified causal structure is consistent with the data, but causal interpretation rests on assumptions that observational data alone cannot verify.