CB-SEM Services
Covariance-based structural equation modeling (CB-SEM) is the confirmatory approach: it tests whether your theoretical model can reproduce the observed data, and reports the global fit that reviewers in confirmatory fields expect. We specify, estimate, and report CB-SEM to a defensible, publishable standard.
CB-SEM (covariance-based structural equation modeling) estimates a structural equation model by trying to reproduce the observed covariance matrix implied by your theory. It is the confirmatory approach—testing how well a hypothesised model fits the data through global fit indices—and is the standard when the goal is to confirm an established theory with reflective constructs.
What CB-SEM does
Structural equation modeling tests a network of relationships among latent constructs measured by observed indicators. CB-SEM is the covariance-based way to do this. Its logic is confirmatory: you specify a model from theory, and the method estimates the parameters that make the model’s implied covariance matrix as close as possible to the observed covariance matrix in your data. How close it gets—the discrepancy between what the model implies and what the data show—is the basis for judging whether the theory holds.
That comparison is expressed through global fit indices: statistics such as CFI, TLI, RMSEA, SRMR, and the chi-square, which together indicate whether the hypothesised model is consistent with the data. This is CB-SEM’s defining feature and its main appeal in confirmatory fields—it provides an overall test of the model, not just individual path estimates. Like PLS-SEM, it has a measurement model (constructs and their indicators) and a structural model (paths among constructs), but it evaluates them against the covariance structure rather than by maximising explained variance.
When to use it
Choose CB-SEM when your goal is confirmatory theory testing—you have a well-developed theoretical model and want to test whether it fits the data and to compare it against competing models—and when your constructs are reflective (indicators caused by the construct). It is the default in psychology, and standard across management and social-science research whenever the emphasis is on confirming theory and reporting global fit.
The decision between CB-SEM and PLS-SEM should turn on your research goal and construct types, not on sample size. If your aim is prediction, your model is very complex, or you have formative constructs, PLS-SEM is the better fit. If you are testing and comparing established theories with reflective measures and want a global fit test, CB-SEM is the appropriate choice—and we help you make and justify that choice.
CB-SEM vs PLS-SEM
| CB-SEM (covariance-based) | PLS-SEM (variance-based) | |
|---|---|---|
| Primary goal | Confirmatory theory testing | Prediction & theory development |
| What it optimises | Reproducing the covariance matrix | Explained variance of outcomes |
| Constructs | Reflective | Reflective & formative |
| Evaluation | Global fit indices (CFI, RMSEA…) | Measurement + structural criteria |
| Assumptions | Larger samples, distributional | Fewer distributional assumptions |
Measurement first, fit reported honestly
A credible CB-SEM follows the two-step approach: establish the measurement model before interpreting the structural model. That means fitting a confirmatory factor analysis first—checking factor loadings, reliability, convergent validity, and discriminant validity—so that the constructs are sound before any path between them is estimated. Structural paths between poorly measured constructs are not interpretable, however good the overall fit looks.
Reporting model fit requires judgement, not a single number. We report a range of indices (CFI, TLI, RMSEA, SRMR, and the chi-square) against accepted thresholds, rather than cherry-picking the one that looks best, and we treat modification indices with caution—data-driven respecification that is not theory-justified is a form of overfitting that will not replicate. CB-SEM also assumes an adequate sample and, in its standard estimator, multivariate normality; where those do not hold, we use robust estimators (such as MLR) or appropriate alternatives and say so.
Good fit is necessary, not sufficient. A model can fit well and still be theoretically wrong or over-fitted through modification indices. We report multiple fit indices honestly, justify any respecification by theory, and validate the measurement model before interpreting a single path.
Software
We deliver CB-SEM in the established tools—R’s lavaan, Mplus, and AMOS—with the full fit-index set, robust estimation where needed, and reproducible, versioned code and output.
How we deliver a CB-SEM analysis
CB-SEM sits within our wider SEM & Psychometrics practice—so the model is specified from theory, the measurement is validated first, and the fit is reported the way confirmatory reviewers expect.
We start from your theoretical model, specify the measurement and structural models, and justify CB-SEM over PLS-SEM for your goal. We fit and validate the measurement model (CFA) first—loadings, reliability, convergent and discriminant validity—then estimate the structural model with a suitable, robust-where-needed estimator.
Reporting follows standard CB-SEM conventions: the full set of fit indices, parameter estimates, and any justified respecification, all transparently presented.
You receive the validated measurement model, the structural results with fit indices and parameter estimates, comparison of competing models where relevant, any mediation or moderation tested, and reproducible code and output. The result is a confirmatory model you can defend in review—fit reported in full, measurement established, respecification justified.
CB-SEM across Management & Allied Studies
CB-SEM is the standard confirmatory tool wherever established theories with reflective constructs are tested—and we apply it across the disciplines we serve.
Applied & Organisational Psychology
The default setting for CB-SEM—confirmatory testing of theories linking attitudes, well-being, and behaviour with reflective measures.
Management & Organisational Studies
Testing and comparing established multi-construct theories of behaviour, performance, and attitudes.
Marketing & Consumer Research
Confirmatory models of established constructs—satisfaction, trust, loyalty—with global fit reported.
Education & Learning Sciences
Confirmatory models of motivation, engagement, and achievement with validated reflective scales.
Health & Behavioural Science
Testing theoretical models of behaviour and well-being where confirmatory fit and reflective measurement matter.
Economics & Public Policy
Confirmatory latent-variable models where the aim is to test theory rather than predict, with reflective constructs.
CB-SEM: common questions
Testing a theoretical model?
If your aim is to confirm an established theory with reflective constructs and report global fit, CB-SEM is the appropriate choice. We specify, validate, estimate, and report it to a standard that holds up in confirmatory review.