ABSTRACT

Partial Least Squares Structural Equation Modeling (PLS-SEM) has grown substantially, marked by fervent scholarly debates and methodological advancements. However, the fundamental issue of non-orthogonal measurement errors is a formidable challenge. This thorough review distills the intellectual conversations, accentuating the hurdles of measurement inaccuracies and the complicated interaction of non-orthogonal latent variables and indicators within the PLS-SEM framework. Despite recent advancements like Consistent PLSc, the intricacies of measurement errors remained inadequately addressed. Existing discussions predominantly orbit around latent variable models, excluding the profound impact of measurement inaccuracies on research outcomes. Moreover, prevalent guidelines lack the nuanced provisions necessary to navigate the labyrinth of non-orthogonal latent variables, a direct fallout of measurement errors, thereby undermining the robustness of PLS-SEM.

This study introduces innovative methodologies to enhance the effectiveness of PLS-SEM. A new shrinkage method using the Ledoit and Wolf estimator with integration of K-fold crossvalidation to select the optimal shrinkage constant is proposed to address non-orthogonality issues, offering a data driven solution for dealing with the complexities associated with nonorthogonal variables. Furthermore, a sophisticated machine learning algorithm utilizing Gradient Descent Optimization is developed and incorporated into the four-step procedure of PLS-SEM. This integration allows PLS-SEM to leverage the advantages of supervised machine learning algorithms. Exploiting the shrinkage method in addressing measurement errors and an enhanced machine learning gradient optimization approach to PLS-SEM represents an evolved iteration of traditional PLS-SEM methodology. This modification ensures a more precise emulation of real-world scenarios, enhancing the model’s accuracy and applicability in complex data environments.

To validate these advanced techniques, extensive simulations (50,000) are conducted under four different scenarios and with varying levels of measurement errors for each scenario. The sample sizes used are 400, 600, 800, and 1000 to asymptotically evaluate the robustness of these methods. Error metrics, including mean absolute deviation (MAD), root mean square error (RMSE), and mean absolute percentage error (MAPE), are employed as benchmarks for validation.

The results unequivocally demonstrate the efficacy of these methodologies in reducing and effectively managing non-orthogonality arising because of measurement errors, thus fortifying the methodological underpinnings of PLS-SEM applications. Moreover, the findings indicate that the modified algorithm (RGPLS-SEM) outperforms the traditional PLSc method, particularly with increasing non-orthogonality and/or measurement errors and sample sizes. The modified method exhibits stable performance based on the error metrics, whereas the PLSc method demonstrates worsening deviations. Moreover, the study applies the novel approach to real-world issues such as money laundering, corruption, and socio-economic development with the mediating role of the black market in the world, highlighting its significance in the complex realm of data analysis.