Transparent PLS-SEM Estimation for Composite-Based Reflective Models

A transparent and modular implementation of Partial Least Squares Structural Equation Modeling (PLS-SEM) focused on reflective measurement models (Mode A). The package separates estimation, bootstrap inference, and predictive evaluation into independent components, emphasising algorithmic transparency, reproducibility, and researcher-controlled analysis. Methods are based on Tenenhaus, Esposito Vinzi, Chatelin & Lauro (2005) , Hair, Risher, Sarstedt & Ringle (2019) , and Henseler, Ringle & Sarstedt (2015) .

PLSsemEngine: A Transparent PLS-SEM Engine in Base R 📊

Version: 1.3.0 (2026-06-15)

PLSsemEngine provides a transparent, modular, and reproducible implementation of Partial Least Squares Structural Equation Modeling (PLS-SEM), specifically designed for composite-based Mode A estimation of reflective models.

🌟 Purpose and Philosophy

The software prioritizes:

• Algorithmic Transparency: Implementation via pure base R matrix operations to ensure long-term stability.
• Methodological Bridges: Native integration with lavaan for CB-SEM/CFA cross-validation.
• Explicit Analytical Control: No hidden heuristics or automatic re-specifications; interpretive support is optional and researcher-led.
• Modular Architecture: Clear separation between estimation, inference, and prediction components.

⚙️ Computational Workflow

The engine follows a standardized and inspectable PLS-SEM pipeline:

1. Data Standardization: Handles mean-centered and standardized scales.
2. Iterative Mode A Estimation: Factorial weighting scheme by default.
3. Measurement Evaluation: Loadings, CR, AVE, HTMT, and HTMT2.
4. Structural Estimation: Path coefficients via OLS on latent scores with $f^2$ effect sizes.
5. Inference: Non-parametric percentile bootstrap for structural significance.
6. Prediction: Strict k-fold cross-validation following the PLSpredict protocol.
7. Model Fit: Assessment via SRMR, $d_{ULS}$, and $d_G$.

Note: Deterministic sign alignment is implemented to ensure stability across resamples and eliminate sign indeterminacy.

🚀 What's New in V1.3.0 (Response to Reviewers)

• Methodological Bridge: Added export_lavaan_syntax() to translate PLS specifications for lavaan.
• Interpretive Layer: Added interpret_model() for diagnostic guidance based on established literature without forcing mechanical decisions.
• Advanced Metrics: Implemented HTMT2 for congeneric models and global fit indices (SRMR, $d_{ULS}$, $d_G$).
• Professional Packaging: The software is now a fully versioned R package installable via devtools.
• Inferential Prediction: Added cvpat() implementing the Cross-Validated Predictive Ability Test (Liengaard et al., 2021; Sharma et al., 2023) for inferential testing of predictive superiority over a naive benchmark.

🛠️ Minimal Example

# Install and load the engine
# devtools::install_github("msoto-perez/PLSsemEngine")
library(PLSsemEngine)

# 1. Generate data
set.seed(123)
data <- data.frame(
  SQ1=rnorm(100), SQ2=rnorm(100), SQ3=rnorm(100),
  CS1=rnorm(100), CS2=rnorm(100), CS3=rnorm(100),
  CL1=rnorm(100), CL2=rnorm(100), CL3=rnorm(100)
)

# 2. Define Models using Native R structures
mm <- list(
  Quality = c("SQ1", "SQ2", "SQ3"),
  Satisfaction = c("CS1", "CS2", "CS3"),
  Loyalty = c("CL1", "CL2", "CL3")
)

sm <- list(
  Satisfaction ~ Quality,
  Loyalty ~ Satisfaction + Quality
)

# 3. Run Analysis
model <- pls_sem(data=data, measurement_model=mm, structural_model=sm)

# 4. Methodological Bridge & Interpretation
export_lavaan_syntax(mm, sm)
interpret_model(model)

# 5. View Results
print(model$tables$table4)  # Structural Paths

📖 Citation If you use this software, please cite:

Manuscript: Soto-Perez, M. (2026). A transparent PLSsemEngine for composite-based Mode A estimation of reflective models in R. SoftwareX. (Under review) .

Software Archive: Soto-Perez, M. (2026). PLSsemEngine (Version 1.3.0). Zenodo. https://doi.org/10.5281/zenodo.20703909

✉️ Contact Dr. M. Soto-Perez Email: [email protected]

Universidad Panamericana, Mexico.