Structural Equation Modeling (SEM)
Structural Equation Modeling · Also known as: Yapısal Eşitlik Modellemesi (SEM), structural equation modelling, covariance structure analysis, latent variable modeling
Structural equation modeling is a multivariate statistical framework that simultaneously estimates a measurement model — relating observed indicators to latent constructs — and a structural model specifying directional or reciprocal relationships among those constructs. Rooted in the LISREL tradition developed by Karl Jöreskog in the 1970s, SEM is the standard tool for testing complex theoretical models in the social, behavioural, and management sciences.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
+10 more
When to use it
SEM is appropriate when your research question involves latent constructs measured by multiple indicators and you want to test a theoretically motivated causal or associational model among those constructs — including mediation, moderation with latent variables, or multi-group comparisons. Several conditions must be met. The measurement model must have been validated with CFA first, establishing convergent validity (factor loadings ≥ 0.50, AVE ≥ 0.50) and discriminant validity. The sample should be at least 300 cases, with a common guideline of 10 observations per estimated parameter and a minimum of three indicators per latent construct to avoid identification problems. Multivariate normality is assumed for standard ML estimation; the MLR estimator relaxes this requirement for moderate departures. The model structure must be specified from theory before looking at the data: SEM is a confirmatory, not exploratory, tool.
Strengths & limitations
- Estimates measurement error and structural relationships simultaneously, yielding unbiased path coefficients that regression cannot provide when constructs are latent.
- Handles complex theoretical structures — mediation chains, reciprocal paths, multi-group invariance — within a single, unified analysis.
- Provides a rich set of fit indices that allow the overall model–data compatibility to be evaluated and compared across competing specifications.
- Widely accepted in social and management sciences, with well-established reporting conventions that facilitate peer review.
- Requires large samples (≥ 300) that may be difficult to obtain in specialised or clinical populations.
- Model fit can often be improved mechanically via modification indices, risking capitalisation on chance if changes are not grounded in theory.
- Results are sensitive to the quality of the measurement model; a poorly specified CFA contaminates the structural estimates.
- Non-convergence and improper solutions (negative variances, correlations > 1) are common with small samples or overparameterised models.
Frequently asked
What is the difference between SEM and path analysis?
Path analysis is a special case of SEM in which all variables are observed (measured without error) and there is no measurement model. SEM generalises path analysis by allowing the causal variables to be latent constructs estimated from multiple indicators, thereby correcting for measurement error. If your constructs are each measured by a single, perfectly reliable indicator, SEM reduces to path analysis.
Do I need to run CFA before SEM?
Yes. A two-step strategy is strongly recommended: first validate the measurement model with CFA to confirm that each latent construct is reliably and distinctly measured, then proceed to the structural model. Bypassing CFA risks conflating poor measurement with poor structural fit, making results uninterpretable.
Which fit indices should I report?
Report at minimum CFI (≥ 0.95), RMSEA (≤ 0.06, with its 90% confidence interval), and SRMR (≤ 0.08). The model chi-square and its degrees of freedom should also be reported but not relied on alone — it is almost always significant for realistic sample sizes. TLI (≥ 0.95) is a useful additional index because it penalises model complexity.
Can SEM prove causation?
No. SEM tests the compatibility of a hypothesised causal structure with observed covariances, but it cannot distinguish that structure from equivalent models that fit equally well. Causal claims require strong theoretical justification, ideally longitudinal or experimental designs, not cross-sectional covariance data alone.
Sources
- Hair, J. F., Black, W. C., Babin, B. J. & Anderson, R. E. (2019). Multivariate Data Analysis (8th ed.). Cengage Learning. ISBN: 978-1473756540
- Kline, R. B. (2016). Principles and Practice of Structural Equation Modeling (4th ed.). The Guilford Press. ISBN: 978-1462523344
- Byrne, B. M. (2012). Structural Equation Modeling with Mplus: Basic Concepts, Applications, and Programming. Routledge. DOI: 10.4324/9780203807644 ↗
How to cite this page
ScholarGate. (2026, June 1). Structural Equation Modeling. ScholarGate. https://scholargate.app/en/statistics/sem
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Confirmatory factor analysisPsychometrics↔ compare
- EFAStatistics↔ compare
- Mediation AnalysisStatistics↔ compare
- Multilevel ModelingResearch Statistics↔ compare
- Path AnalysisStatistics↔ compare