Structural equation modelling (SEM) is one of the most popular techniques in management, education, psychology and social science theses. It lets you test a whole model of relationships at once, including concepts you cannot measure directly, such as trust, satisfaction or intention. It is also easy to get wrong. This guide explains the essentials.
What SEM does
SEM combines two ideas:
- A measurement model: how well your questionnaire items (indicators) measure each latent construct. This is confirmatory factor analysis (CFA)
- A structural model: how the constructs affect each other, such as service quality leading to satisfaction, and satisfaction leading to loyalty
Always assess the measurement model first. If your constructs are not measured reliably and validly, the relationships between them mean little.
CB-SEM or PLS-SEM?
| CB-SEM (covariance-based) | PLS-SEM (partial least squares) | |
|---|---|---|
| Main aim | Testing and confirming a theory | Prediction and exploring or extending a theory |
| Typical software | AMOS, lavaan (R), Mplus, LISREL | SmartPLS, SEMinR (R) |
| Sample size | Usually larger (often 200 or more) | Works with smaller samples, though power still matters |
| Data | Assumes approximately normal data (robust options exist) | No normality assumption; significance by bootstrapping |
| Model fit | Global fit indices are central | Focus on explained variance and prediction |
Choose by your research aim and data, and say why in your methodology. Choosing PLS-SEM only because the sample is small, without other reasons, is a choice reviewers increasingly question.
Sample size
Rules of thumb vary. The old "10 times rule" for PLS-SEM (ten cases per arrow pointing at a construct) is now considered too lenient. Better approaches are a power analysis for the most complex part of your model, or the inverse square root method for PLS-SEM. Plan for a comfortable margin, because some responses will be incomplete.
Checking the measurement model
Commonly used thresholds (cite the sources you follow, and treat them as guides, not laws):
- Indicator loadings: 0.70 or above is ideal; items between 0.40 and 0.70 can be kept if reliability and validity are fine
- Internal consistency: Cronbach's alpha and composite reliability of 0.70 or more
- Convergent validity: average variance extracted (AVE) of 0.50 or more (Fornell and Larcker, 1981)
- Discriminant validity: the heterotrait-monotrait ratio (HTMT) below 0.85, or 0.90 for conceptually similar constructs (Henseler, Ringle and Sarstedt, 2015). The older Fornell-Larcker criterion is often reported too
Model fit in CB-SEM
Report several indices together, not just the ones that look good. Widely cited cut-offs from Hu and Bentler (1999) are:
- CFI and TLI: 0.95 or above (0.90 is often treated as acceptable)
- RMSEA: 0.06 or below (up to 0.08 acceptable)
- SRMR: 0.08 or below
The chi-square test is usually reported too, though it is sensitive to large samples. Do not "improve" fit by adding error correlations without a theoretical reason.
Testing the structural model
- Path coefficients with their significance (in PLS-SEM, from bootstrapping, commonly with 5,000 subsamples)
- R squared for each outcome: how much of it the model explains
- Effect sizes (f squared) and, in PLS-SEM, predictive relevance (such as Q squared or PLSpredict)
- Collinearity between predictors (VIF values)
Mediation and moderation
SEM handles both well. For mediation, test the indirect effect directly with bootstrapped confidence intervals rather than the older step-by-step approach. For moderation, use an interaction term or a multi-group analysis, and check measurement invariance before comparing groups.
Common mistakes
- Skipping the measurement model and going straight to hypotheses
- Ignoring common method bias when all data come from one questionnaire (check it, for example with a marker variable or a full collinearity test)
- Reporting only the indices that pass
- Drawing a model without a theory behind each arrow
- Claiming cause from cross-sectional survey data
How to report it
Include a figure of the model, a table of loadings, reliability and validity, a discriminant validity table, the fit indices (CB-SEM) and a table of hypotheses with path coefficients, t or z values, p-values and whether each is supported.
Our data analysis service runs and explains CB-SEM in AMOS and PLS-SEM in SmartPLS, and our workshops often cover them hands-on. New to statistics? Start with choosing the right statistical test.
