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Modified partial least square structural equation model with multivariate adaptive regression spline: Parameter

Hendra H Dukalang1,2, Bambang Widjanarko Otok1, Purhadi1

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This study introduces Multivariate Adaptive Regression Splines Partial Least Square (MARSPLS) to address nonlinearities in Partial Least Squares Structural Equation Modelling (PLS-SEM). MARSPLS enhances predictive accuracy for complex latent variable relationships.

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Area of Science:

  • Statistics
  • Machine Learning
  • Behavioral Science

Background:

  • Partial Least Squares Structural Equation Modelling (PLS-SEM) often yields biased results due to its linear assumptions.
  • Capturing nonlinear and interaction effects between latent variables is a significant challenge in existing PLS-SEM models.

Purpose of the Study:

  • To propose a novel model, Multivariate Adaptive Regression Splines Partial Least Square (MARSPLS), to overcome the limitations of PLS-SEM in handling nonlinear relationships.
  • To enhance the predictive accuracy of structural equation modeling by incorporating the flexibility of Multivariate Adaptive Regression Splines (MARS).

Main Methods:

  • The MARSPLS model integrates MARS within the PLS-SEM framework to capture nonlinear and interaction effects.
  • Parameter estimation for MARSPLS is detailed using Maximum Likelihood Estimator (MLE) and Ordinary Least Squares (OLS).
  • The model's performance is validated using simulated data and empirical data on e-wallet behavioral intention from 385 Indonesian respondents.

Main Results:

  • MARSPLS with interaction demonstrated superior predictive accuracy compared to traditional methods.
  • The model achieved a higher R² value of 54.08% and lower information criteria (AIC, AICc) and Root Mean Square Error (RMSE).

Conclusions:

  • MARSPLS offers a novel approach for PLS-SEM when latent variable relationships are nonlinear or unknown.
  • The proposed method effectively models complex relationships involving four exogenous and one endogenous latent variable, without moderation or mediation effects.