Exploratory Structural Equation Modeling
Also known as: ESEM
Exploratory Structural Equation Modeling (ESEM) is a hybrid approach that combines exploratory factor analysis (EFA) with confirmatory factor analysis (CFA) and path modeling, developed by Asparouhov and Muthén (2009). ESEM relaxes restrictive zero-loading assumptions of traditional CFA, allowing all indicators to load on all factors, which can reveal cross-factor complexity and improve model fit while retaining the ability to test substantive structural theories.
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When to use it
Apply ESEM when factor structures are complex or not well understood, when measurement models may have substantial cross-loadings, or when you want to simultaneously explore measurement and test structural relationships. Ideal for multi-dimensional psychological constructs and when traditional CFA fits poorly due to restrictive assumptions.
Strengths & limitations
- Flexible measurement: allows cross-loadings, capturing more nuanced factor structures than restrictive CFA
- Better fit: often achieves better model fit than CFA while remaining interpretable
- Integrated exploration and confirmation: combines strengths of EFA (exploratory) and CFA/SEM (confirmatory) in one model
- Reduced bias: relaxing zero-loading constraints can reduce bias in parameter estimates, particularly for structural paths
- Transparent complexity: reveals cross-dimensional relationships that traditional CFA hides
- Model complexity: more parameters than CFA models, requiring larger samples for stable estimation
- Interpretation difficulty: cross-loadings can complicate interpretation of what each factor represents
- Comparison challenges: difficult to compare models with different numbers of cross-loadings using standard fit indices
- Software requirements: not all SEM software supports ESEM; limited to specialized packages like Mplus or lavaan
Frequently asked
When should I use ESEM instead of traditional CFA?
Use ESEM when traditional CFA fits poorly, when indicators show substantial cross-loadings, or when factors are theoretically complex and multidimensional. CFA is more parsimonious; ESEM trades simplicity for better fit when warranted.
What do cross-loadings mean?
Cross-loadings indicate that an indicator is related to multiple latent factors, not just its primary factor. They can reflect genuine construct overlap, measurement imprecision, or conceptual complexity. High cross-loadings suggest the item measures multiple constructs.
How do I choose a rotation method in ESEM?
Common rotations include Geomin (encourages sparse loadings), Quartimin (encourages independent factors), and target rotation (specify expected loadings). Geomin is default in many software packages. Try multiple and compare interpretability and theoretical alignment.
How large a sample do I need for ESEM?
With many cross-loadings allowed, ESEM requires larger samples than traditional CFA. A rule of thumb is at least 20-30 cases per parameter estimated. For complex models, 200-500+ cases is recommended.
Can I test measurement invariance with ESEM?
Yes. You can specify ESEM with constraints across groups (e.g., across countries or time points) to test whether factor structures are equivalent. This is more flexible than traditional CFA invariance testing.
Sources
- Asparouhov, T., & Muthén, B. (2009). Exploratory structural equation modeling. Structural Equation Modeling, 16(3), 397-438. DOI: 10.1080/10705510903008204 ↗
- Marsh, H. W., Lüdtke, O., Muthén, B., Asparouhov, T., Morin, A. J., Trautwein, U., & Nagengast, B. (2010). A new perspective on structural equation modeling: Guest editors' introduction. Structural Equation Modeling, 17(3), 357-370. link ↗
- Muthén, B., & Asparouhov, T. (2012). Bayesian structural equation modeling: A more flexible representation of substantive theory. Psychological Methods, 17(3), 313-335. DOI: 10.1037/a0026802 ↗
How to cite this page
ScholarGate. (2026, June 3). Exploratory Structural Equation Modeling. ScholarGate. https://scholargate.app/en/psychometrics/exploratory-structural-equation-modeling
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