Overview
CB-SEM jointly estimates a validated reflective measurement model and a researcher-specified recursive latent structural model.
Theoretical foundation
The structural model relates endogenous latent variables to other latent variables and disturbances. Direct effects are structural coefficients; indirect effects are products and sums across directed paths; total effects combine direct and indirect effects.
Key equations
\eta=B\eta+\Gamma\xi+\zetaAlgorithm and computation
Survlytics reuses an approved CFA revision, accepts only acyclic directed construct paths, includes covariances among exogenous factors, and fits the joint model through semopy MLW/SLSQP on listwise-complete continuous indicators. It reports fit, standardised and unstandardised paths, direct/indirect/total effects, latent R², residuals, convergence and admissibility.
Required data
An approved CFA measurement model, identified reflective constructs, at least one acyclic structural path and sufficient complete continuous-indicator observations.
Assumptions
The measurement model is credible, the recursive path structure is theory-defined, observations are independent, and normal-theory ML is suitable.
Available settings
Approved measurement-model revision; recursive path specification; confidence/display settings inherited from the validated workflow.
Worked example
The frozen benchmark uses three latent factors and paths F1 → F2, F1 → F3 and F2 → F3 for N = 800 synthetic observations.
Limitations and non-claims
No feedback loops, categorical outcomes, robust ML, FIML, equality constraints, multigroup SEM or causal identification are implemented. Arrows do not establish causality.
Validation notes
A frozen R 4.5.2/lavaan 0.7-2 fixture compares fit, paths, loadings, indirect/total effects and latent R². Fit and standardised estimates use absolute tolerance 0.002; AIC/BIC use 0.02.
How Surv.lytics computes Covariance-based SEM
{'estimator': 'MLW', 'recursive': True}PASS: frozen reference statistics agree within the declared tolerances. Tolerance: 0.002 for fit/standardised estimates; 0.02 for AIC/BIC Known differences: Only supported recursive continuous-indicator models are covered.
References and verification status
Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39–50. https://doi.org/10.2307/3151312
VerifiedOpen DOIHu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55. https://doi.org/10.1080/10705519909540118
Unverified draftOpen DOI
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