Structural Equation Modelling

Definition

Structural equation modelling is a multivariate statistical technique that combines factor analysis and regression analysis to test complex relationships among observed and latent variables. It allows researchers to specify and estimate path models, mediation effects, and measurement models simultaneously within a single integrated framework.

Why It Matters

Many theoretical models in psychology, education, and social science involve chains of cause-and-effect relationships that cannot be tested adequately with simple regression. SEM provides a rigorous way to evaluate whether the data support an entire theoretical model at once, including both direct and indirect effects. It is the method of choice for validating psychometric instruments and testing causal hypotheses in cross-sectional and longitudinal data.

Example

An organisational researcher proposes that job autonomy influences employee well-being both directly and indirectly through work engagement. She measures autonomy with three survey items, engagement with four items, and well-being with three items. A structural equation model estimates the direct path from autonomy to well-being (β = 0.25, p = 0.01) and the indirect path via engagement (β = 0.18, p = 0.02). The model fit indices (CFI = 0.96, RMSEA = 0.05) indicate the data fit the theoretical structure well.

Related Terms

• Factor Analysis
• Construct Validity
• Regression Analysis
• Cronbach's Alpha
• Multilevel Modelling (for nested data, SEM can be extended to multilevel SEM)

Software Notes

• SPSS: SPSS does not have a built-in SEM module. The standard approach is to use AMOS (included with SPSS Statistics Premium) via Analyze > AMOS or the standalone AMOS Graphics interface.
• R: lavaan::sem(model, data = df) is the most popular SEM package. semPlot::semPaths() draws path diagrams. Fit indices: fitMeasures(model) returns CFI, TLI, RMSEA, SRMR.
• Stata: sem (wellbeing <- engagement autonomy) (engagement <- autonomy) for path models. gsem for generalised SEM with categorical or count outcomes. estat gof reports goodness-of-fit statistics.