I built the same model on ADANCO and SmartPLS and went to check how they differed for the fit criteria values such as SRMR, R², pA, pC, and AVE. The model's weights don't differ too much between ADANCO and SmartPLS, ranging from a 5% interval. SRMR and pA had less thana 1% difference average between the different models, but pC had 7.6%, and R² and AVE had an almost 12.5% average disparity, with a 0,073 and 0,049 standard deviation, respectively.
What could be inferred by this? Is there an issue with the models I'm using? Do ADANCO and SmartPLS use different
The differences in R² (coefficient of determination) and pC (path coefficients) between ADANCO and SmartPLS for the same structural equation models (SEM) can arise from several methodological and algorithmic factors. Here are the key reasons:
1. Algorithmic Differences
ADANCO uses consistent PLS (PLSc), which corrects for measurement error in reflective constructs to provide asymptotically consistent estimates (similar to covariance-based SEM).
SmartPLS defaults to traditional PLS-SEM, which prioritizes prediction over consistency, potentially inflating R² and path coefficients due to ignored measurement error.
Example: PLSc in ADANCO adjusts for attenuation bias, often leading to lower R² and pC values compared to SmartPLS.
2. Handling of Reflective vs. Formative Constructs
ADANCO strictly follows Dijkstra-Henseler’s PLSc for reflective constructs, which modifies weight and loading calculations.
SmartPLS applies traditional PLS, which can overestimate relationships for reflective constructs but handles formative constructs more straightforwardly.
Impact: Models with reflective constructs will show larger discrepancies.
3. Bootstrapping Procedures
ADANCO and SmartPLS may use different:
Resampling methods (e.g., cases vs. residuals).
Default bootstrap samples (e.g., 5,000 in ADANCO vs. 1,000 in SmartPLS).
Result: p-values and confidence intervals for pC can vary, especially with small samples.
4. Correction for Measurement Error
ADANCO automatically corrects for composite reliability (ρA) in PLSc, reducing bias in pC.
SmartPLS (unless using PLSc mode) does not apply this correction, leading to higher (but potentially biased) coefficients.
5. Standardization Approaches
Differences in how latent variables are standardized (e.g., unit variance vs. marker variable scaling) can affect coefficient magnitudes.
ADANCO often uses correlation-based standardization, while SmartPLS may default to regression-based scaling.
6. Convergence Criteria
Stopping rules for the PLS algorithm (e.g., tolerance levels, max iterations) differ between software, leading to slight variations in final estimates.
https://eli.johogo.com/Class/CCU/SEM/_A%20Primer%20on%20Partial%20Least%20Squares%20Structural%20Equation%20Modeling_Hair.pdf
https://www.ijbs.unimas.my/images/repository/pdf/Vol19-no1-paper10.pdf
Raphael Alexsander Prado dos Santos : There can be many reasons for different outcomes, for instance, the dataset used and its missing data treatment, the selection of settings, the treatment of binary variables etc.
We do not use ADONCO. However, here is a PLSc-SEM example in the R package "SEMinR": https://cran.r-project.org/web/packages/seminr/
library(seminr)
# Load your data, here we just use the mobi dataset that comes with seminr
mobi
You can run the same model in SmartPLS (i.e., the ECSI sample project). Use the consistent PLS-SEM algorithm to receive the PLSc-SEM outcomes. As you can see, the SmartPLS results are identical compared with the R results:
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