The consistent PLS (PLSc) algorithm performs a correction of reflective constructs' correlations to make results consistent with a factor-model (Dijkstra 2010; Dijkstra 2014; Dijkstra and Henseler 2015; Dijkstra and Schermelleh-Engel 2014).

Initial Calculations:

One can decide whether the initial PLS path model should be taken as it is or if all LVs should be connected to generate latent variable scores when running the PLS algorithm. Dijkstra and Henseler (2012) advised to use connections between all LVs for the estimation of the latent variables scores to get more stable results.

Until now, no additional parameter specifications are required for the correction that PLSc performs on the results of the basic PLS algorithm. However, parameter settings for the underlying PLS algorithm are important and should be checked.

Consistent bootstrapping uses the consistent PLS algorithm. Bootstrapping is a nonparametric procedure that allows testing the statistical significance of various PLS-SEM results such path coefficients, Cronbach’s alpha, HTMT, and R² values.

Steps in Assessing GoF

Step 1: Run Consistent PLS Algorithm.

Step 2: Assess the fit summary result using the Consistent PLS Algorithm output.

Step 3: Check at the SRMR and NFI for both saturated and estimated models and compare the values with the threshold values. If the researchers are interested in RMS_Theta, they can opt for PLS Algorithm execution rather than consistent PLS Algorithm (only if the researchers assume to study a composite model rather than a factor model).

Step 4: Run Consistent PLS Bootstrapping, select complete bootstrapping, one-tailed test, and make sure the significance level is 0.05 (as suggested by Henseller et al., 2016).

Step 5: Click on bootstrapping results, select d_ULS and interpret the results for both saturated and estimated models. When p-values < 0.05, then the estimated model does not fit the data.

Step 6: Click on Confidence interval results for d_ULS. If all discrepancies for both saturated and estimated models exceed 95% percentile of their bootstrap distribution, then the empirical and the model-implied correlation matrices do differ significantly because the values are greater that Hi95. In other words, the model does not fit the data.

Step 7: Repeat step 5 and 6 for d_G.

Note: If the results demonstrate that all discrepancies exceed the 95% percentile of the bootstrap distribution for d_ULS and d_G (lead to the rejection of model), then another alternative is to opt for the 99% percentile of the bootstrap distribution.

Is the assessment of GoF compulsory in PLS-SEM?

"... the choice of using GOF is still in a very early stage and it is not compulsory to apply in the context of PLS-SEM"..., we are strongly against researchers who feel uncomfortable without the absolution and present through a global index because blindly practicing statistical techniques will harm the overall study..." (Ramayah et al., 2018)

The distinction of estimated and saturated models in PLS-SEM is in its very early stages. Future research must provide detailed explanations and recommendations on the computation, usage and interpretation of these outcomes.

The saturated model assesses correlation between all constructs. The estimated model is a model which is based on a total effect scheme and takes the model structure into account. It is hence a more restricted version of the fit measure.

Researchers often struggle to choose between the estimated and saturated model when trying to report the fit of a PLS path model. At this stage, PLS-SEM literature is very vague on the use of fit criteria in general and, in specific, the choice between the estimated and saturated model. However, the estimated model seems to be a reasonable choice, if a researcher makes the questionable decision to report the fit results of the PLS path model.

Source: https://www.smartpls.com/documentation/algorithms-and-techniques/model-fit/

Cho, G., Hwang, H., Sarstedt, M., & Ringle, C. M. (2020). Cutoff criteria for overall model fit indexes in generalized structured component analysis. Journal of Marketing Analytics. doi:10.1057/s41270-020-00089-1. Click here.

Dijkstra, T. K. (2010). Latent Variables and Indices: Herman Wold’s Basic Design and Partial Least Squares, in Handbook of Partial Least Squares: Concepts, Methods and Applications (Springer Handbooks of Computational Statistics Series, vol. II), V. Esposito Vinzi, W. W. Chin, J. Henseler and H. Wang (eds.), Springer: Heidelberg, Dordrecht, London, New York, pp. 23-46.

Dijkstra, T. K. (2014). PLS' Janus Face – Response to Professor Rigdon's ‘Rethinking Partial Least Squares Modeling: In Praise of Simple Methods’, Long Range Planning, 47(3): 146-153. Click here.

Dijkstra, T. K., and Henseler, J. (2015). Consistent Partial Least Squares Path Modeling, MIS Quarterly, 39(2): 297-316. Click here.

Dijkstra, T. K., and Schermelleh-Engel, K. (2014). Consistent Partial Least Squares for Nonlinear Structural Equation Models, Psychometrika, 79(4): 585-604. Click here.

Henseler, J., & Sarstedt, M. (2013). Goodness-of-fit indices for partial least squares path modeling. Computational Statistics, 28(2), 565-580. Click here.

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