If your research model has several constructs, each measured by multiple questionnaire items, and paths between them, you need structural equation modeling (SEM). Then comes the question every thesis student and reviewer asks: CB-SEM or PLS-SEM?
Both estimate a measurement model (items → constructs) and a structural model (construct → construct) at the same time. But they are built on different statistical philosophies, answer slightly different questions, and are judged by different criteria. This guide lays out the differences, gives a decision checklist, and points to free software for both.
- CB-SEM reproduces the covariance matrix of your items. It is the classic choice for testing and confirming theory, and it gives global fit indices such as CFI and RMSEA.
- PLS-SEM maximizes the explained variance of the outcome constructs. It is suited to prediction, complex models, formative constructs and exploratory theory development.
- Choose based on your research goal and construct type, not just your sample size.
In this guide
What is CB-SEM?
Covariance-based SEM (the approach behind AMOS, lavaan, Mplus and LISREL) estimates model parameters so that the covariance matrix implied by your model is as close as possible to the observed covariance matrix, usually by maximum likelihood (ML). Constructs are treated as common factors: latent variables that cause their items, with measurement error modelled explicitly.
Because it reproduces the whole covariance matrix, CB-SEM gives a chi-square test and global fit indices (CFI, TLI, RMSEA, SRMR) that tell you whether your theory, as specified, is consistent with the data. See our explainer on model fit indices.
What is PLS-SEM?
Partial least squares SEM (the approach behind SmartPLS, ADANCO and the R package seminr) builds each construct as a weighted composite of its items, then estimates the paths with a series of regressions. The algorithm aims to maximize the R² of the endogenous constructs. Significance comes from bootstrapping, because PLS makes no distributional assumptions.
PLS-SEM has no exact global fit test comparable to CB-SEM's chi-square. Instead, you evaluate the model on reliability, validity, R², f², Q² and out-of-sample predictive power (PLSpredict). SRMR is sometimes reported, but its thresholds for PLS are debated.
Side-by-side comparison
| CB-SEM | PLS-SEM | |
|---|---|---|
| Main goal | Theory testing and confirmation | Prediction and explanation of variance; theory development |
| Construct type | Common factors (reflective) | Composites; reflective and formative |
| Estimation | Maximum likelihood (and robust variants) | Iterative OLS regressions |
| Global fit | χ², CFI, TLI, RMSEA, SRMR | No exact global fit test; SRMR sometimes used |
| Significance testing | Analytic standard errors | Bootstrapping |
| Distributional assumptions | Multivariate normality for ML (robust corrections available) | None (non-parametric bootstrap) |
| Sample size | Usually 200+; depends on model complexity | Can work with smaller samples, but power still matters |
| Model complexity | Can struggle with very large models | Handles many constructs and indicators |
| Formative constructs | Possible but tricky (identification issues) | Straightforward |
| Typical software | AMOS, lavaan, Mplus | SmartPLS, ADANCO, seminr |
| Free in-browser option | CB-SEM Studio | PLS-SEM Studio |
Decision checklist
Choose CB-SEM if:
- your goal is to test or confirm an established theory;
- your constructs are reflective (items are interchangeable manifestations of the construct);
- reviewers in your field expect CFA and global fit indices (common in psychology, education and much of management);
- you have a reasonable sample (typically 200 or more) and roughly normal data, or you can use robust estimation.
Choose PLS-SEM if:
- your goal is prediction or explaining as much variance as possible in key outcomes;
- your model includes formative constructs (items that define the construct, such as an index of firm resources);
- the model is complex (many constructs, mediators or moderators) or the theory is still developing;
- you need construct scores for follow-up analyses such as importance-performance map analysis (IPMA) or fsQCA.
"Small sample" was once the most common justification for PLS-SEM, and reviewers now push back on it. PLS-SEM can estimate models with small samples, but a small sample still gives low statistical power and unstable estimates. Do a power analysis whichever method you choose.
Reporting differences
Measurement model (both): loadings, Cronbach's alpha, composite reliability (CR), AVE and discriminant validity via HTMT. Our guide to HTMT and Fornell-Larcker covers the last step.
CB-SEM structural model: χ² with df, CFI, TLI, RMSEA (with 90% CI), SRMR, standardized path coefficients with p-values, R², and indirect effects with bootstrap or Monte Carlo CIs.
PLS-SEM structural model: collinearity (inner VIF), path coefficients with bootstrap CIs, R², f², Q² or PLSpredict results, and indirect effects.
Can I run both?
Yes, and it can strengthen a paper: confirm the measurement model with CFA (CB-SEM), then estimate the structural model with the method that fits your goal, or report one as a robustness check of the other. Just make sure the choice is driven by your research question, and say why in your methods section.
Free software for CB-SEM and PLS-SEM
Both approaches run free in your browser on FreeStatisticalTools.com, with no installation and no data upload:
- CB-SEM Studio: draw constructs and paths with a drag-and-drop builder, then run CFA and SEM by maximum likelihood. You get fit indices, reliability and validity tables, mediation with confidence intervals, latent moderation with simple slopes, and modification indices. Start with the CB-SEM tutorial.
- PLS-SEM Studio: the PLS algorithm with bootstrapping, the measurement and structural model, mediation, two-stage moderation, IPMA and fsQCA built in. Start with the PLS-SEM tutorial.
Frequently asked questions
What is the main difference between CB-SEM and PLS-SEM?
CB-SEM estimates a model that reproduces the covariance matrix of the items and is mainly used to test theory with global fit indices. PLS-SEM builds constructs as weighted composites and maximizes explained variance, which makes it suited to prediction, complex models and formative constructs.
Which is better, AMOS or SmartPLS?
Neither is better in general. AMOS is CB-SEM software, so use it, or a free alternative, for confirmatory theory testing with reflective constructs. SmartPLS is PLS-SEM software, so use it, or a free alternative, for prediction-oriented or formative models.
What sample size do I need for CB-SEM?
There is no single number. Around 200 is a common minimum for moderately complex models with ML estimation, and more is needed for complex models, non-normal data or weak loadings. Monte Carlo power analysis gives a model-specific answer.
Does PLS-SEM have model fit indices?
PLS-SEM has no exact global fit test like CB-SEM's chi-square. SRMR is sometimes reported, but the focus is on reliability, validity, R², f² and predictive relevance (Q² and PLSpredict).
Is there a free alternative to AMOS?
Yes. CB-SEM Studio on FreeStatisticalTools.com runs CFA and SEM by maximum likelihood in your browser with a drag-and-drop model builder. In R, the lavaan package is a free, widely used option.