Structural equation modelling (SEM) is the family of methods that tests relationships among latent variables in a single model while separating out measurement error. For most postgraduate researchers the first practical question is software: AMOS or SmartPLS? The honest answer is that the choice is not about software at all but about two statistical traditions — covariance-based SEM (CB-SEM) and variance-based partial least squares SEM (PLS-SEM) — which serve different research questions. This guide summarises the selection criteria and the thresholds you must report in each tradition.
CB-SEM and PLS-SEM: Two philosophies
CB-SEM (AMOS, lavaan, Mplus) belongs to the theory-testing tradition: the model attempts to reproduce the observed covariance matrix, and the fit of the whole model to the data is judged with global fit indices. PLS-SEM (SmartPLS) is prediction-oriented: it maximises the explained variance (R²) of the endogenous constructs and replaces global fit with a chain of quality criteria for the measurement and structural models. The first answers "does my theory contradict the data?"; the second answers "how well does the model predict the target construct?".
When is each approach appropriate?
- Sample size: CB-SEM generally needs 200 or more cases for stable estimation; PLS-SEM can run on smaller samples, but it must not be used as a licence for an underpowered study — a power analysis is still required.
- Distribution: Maximum likelihood estimation in AMOS assumes multivariate normality (with corrections such as the Bollen-Stine bootstrap when it fails); PLS-SEM makes no distributional assumption.
- Construct type: Formative measurement models are specified naturally in PLS-SEM; in CB-SEM they require additional identification constraints.
- Purpose: Choose CB-SEM to confirm mature theory and compare rival models; choose PLS-SEM for complex models at an early theoretical stage where predictive power is the goal.
| Criterion | AMOS / CB-SEM | SmartPLS / PLS-SEM |
|---|---|---|
| Primary aim | Theory testing, model confirmation | Prediction, exploratory modelling |
| Estimation | Maximum likelihood (covariance) | Partial least squares (variance) |
| Sample expectation | Usually ≥ 200 | More flexible; power analysis required |
| Normality assumption | Yes (for ML) | No |
| Formative constructs | Restricted, extra identification needed | Supported directly |
| Evaluation | Global fit indices | Quality criteria (AVE, HTMT, R², f²) |
Fit indices in structural equation modelling: Thresholds
Evaluation in CB-SEM is two-layered: first the measurement model (a CFA — do the items represent their factors well?), then the structural model (the paths among latent variables). The same set of indices is reported for both layers: χ²/df ≤ 3, RMSEA ≤ 0.08 (≤ 0.05–0.06 for good fit), CFI and TLI ≥ 0.90 (≥ 0.95 for good fit), and SRMR ≤ 0.08. The χ² test itself is almost always significant in large samples, so it should never be the sole ground for rejecting a model. For the measurement side in detail, see our guide to scale development with EFA and CFA.
In practice, follow the two-step approach: test the measurement model on its own first, and do not move to the structural paths until it reaches acceptable fit. Interpreting structural coefficients on a weak measurement model is like praising the floor plan of a building with rotten foundations — a seemingly significant path may simply be feeding on error in the item-factor relationships. Once the measurement model is confirmed, specify the structural model, report the fit of both in separate rows, and discuss any marked deterioration between them as a sign that the structural constraints conflict with the data.
Treat modification indices with caution: adding every suggested error covariance improves fit mechanically while overfitting the model and hollowing out its theoretical meaning. Modify only for item pairs within the same subscale that share a wording stem, justify each change in the text, and report fit before and after modification — transparency demands both sets of values.
Quality criteria in SmartPLS
PLS-SEM does not use global fit indices; instead, a sequential quality chain is reported. For the measurement model: outer loadings ≥ 0.70 (items between 0.40 and 0.70 are judged by their contribution to AVE and CR), AVE ≥ 0.50, composite reliability (CR) ≥ 0.70, and for discriminant validity HTMT < 0.85 (relaxed to 0.90 for conceptually close constructs). For the structural model: R² values (roughly 0.25 weak, 0.50 moderate, 0.75 substantial), bootstrap significance of the path coefficients (5,000 resamples), and f² effect sizes (0.02 small, 0.15 medium, 0.35 large). Collinearity is checked by keeping VIF values below 5. Studies making a predictive claim should additionally show that Q² predictive relevance exceeds zero; an endogenous construct with Q² ≤ 0 has no predictive power, and no R², however high, can rescue the claim.
Reporting standards
Whichever tradition you choose, the report must include: the rationale for the method (why CB-SEM, or why PLS-SEM), the sample size and power justification (with G*Power), the estimator, measurement model results (loadings, AVE, CR, discriminant validity), structural model results (standardised coefficients with confidence intervals), and every modification made. Cherry-picking fit indices — reporting only those that clear the threshold — is the problem reviewers catch fastest; always give the standard set in full, following the conventions in our guide to reporting statistics in APA 7. If indirect effects are tested, enable bootstrap confidence intervals in AMOS (5,000 resamples) or report the specific indirect effects table in SmartPLS — see our PROCESS guide for the mediation logic. And if the scale is claimed to work equivalently across groups, add multi-group analysis and measurement invariance tests to the report.
The software question is really a theory question: are you testing your theory, or predicting your target?
Frequently Asked Questions
What sample size do I need for structural equation modelling?
For CB-SEM the common floor is 200 cases, aiming for 5–10 observations per estimated parameter depending on model complexity. PLS-SEM is more flexible, but in both traditions the sample should be justified with a power analysis using a tool such as G*Power.
What should I do if my fit indices fall below the thresholds?
Inspect the measurement model first: low-loading or cross-loading items are the most common cause. Use modification indices only with a theoretical rationale and report every change; adding paths merely to rescue fit turns the model into an exploratory one.
Do I have to report fit indices in SmartPLS?
Global indices such as CFI or RMSEA are not defined in PLS-SEM; SRMR can be given as an approximate indicator. What is expected instead is the complete quality chain: loadings, AVE, CR and HTMT for measurement, then R², f² and bootstrap confidence intervals for the structural model.
What SEM services does Celsus offer?
We advise on model specification and choice of tradition, run the analysis in AMOS, lavaan or SmartPLS, interpret fit indices and quality criteria, guide modification decisions, and prepare journal-ready tables and figures. All outputs are delivered with reproducible files.