Overview
Survlytics implements a recursive PLS path-modelling engine with reflective Mode A and formative Mode B blocks, full-refit bootstrap inference and a separately labelled repeated K-fold prediction assessment.
Theoretical foundation
PLS-PM iteratively constructs standardised composite scores from outer weights, updates inner proxies using the path-weighting scheme, and re-estimates measurement weights until the maximum weight change is below tolerance. Structural paths are OLS regressions among final construct scores.
Key equations
\hat{\eta}_j=X_jw_j\max_j\lVert w_j^{(t)}-w_j^{(t-1)}\rVert_\infty<10^{-7}Algorithm and computation
Indicators are standardised from complete rows. Default tolerance is 1e−7 and maximum iterations 300. Score signs are oriented to correlate positively with their block sums. Mode A updates weights from indicator–proxy correlations; Mode B uses multivariate regression weights. Outputs include weights, loadings, cross-loadings, alpha, composite reliability, rho_A, AVE, HTMT, formative and structural VIF, paths, R²/adjusted R², f², effects and full-refit case bootstrap intervals. Prediction uses fold-local preprocessing and repeated K-fold scoring against a training-mean benchmark.
Required data
Researcher-approved numeric indicator blocks, declared Mode A or Mode B measurement, an acyclic directed construct graph, and at least the validated minimum complete sample.
Assumptions
Measurement mode follows theory; formative and reflective criteria are not interchangeable. Structural interpretation assumes a correctly specified recursive linear composite model.
Available settings
Tolerance; maximum iterations; bootstrap samples/seed/confidence; sign stability; optional prediction folds, repetitions and seed; model-comparison settings.
Worked example
The frozen synthetic benchmark contains three reflective blocks and three recursive paths. Weights, loadings, paths, R² and adjusted R² are compared with R/seminr 2.5.0. A separate mixed Mode A/B fixture checks formative weights and rho_A.
Limitations and non-claims
The prediction routine is not proprietary or published PLSpredict and is never labelled as such. Blindfolding Q² is unavailable. No universal global fit index is claimed. Bootstrap inference remains sample- and model-dependent.
Validation notes
Frozen seminr 2.5.0 fixtures compare weights, loadings, paths, R² and adjusted R² at 1e−7 absolute tolerance, plus a mixed Mode A/B reference and independently frozen holdout scores.
How Surv.lytics computes PLS-SEM
{'tolerance': 1e-07, 'max_iterations': 300}PASS: the reflective fixture agrees with the frozen seminr values; additional mixed Mode A/B and holdout fixtures also pass. Tolerance: Absolute tolerance 1e-7 for weights, loadings, paths and R² Known differences: Survlytics prediction is a separate repeated K-fold protocol and is not labelled PLSpredict.
References and verification status
Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). A new criterion for assessing discriminant validity in variance-based structural equation modeling. Journal of the Academy of Marketing Science, 43(1), 115–135. https://doi.org/10.1007/s11747-014-0403-8
VerifiedOpen DOIWold, H. (1982). Soft modeling: The basic design and some extensions. Systems under indirect observation, Part II.
Unverified draft
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