Modified partial least square structural equation model with multivariate adaptive regression spline: Parameter estimation technique and applications

Partial Least Squares Structural Equation Modelling (PLS-SEM) struggles with nonlinear relationships between latent variables, leading to biased results. To address this limitation, this study proposes a new model, Multivariate Adaptive Regression Splines Partial Least Square (MARSPLS), which is based on Multivariate Adaptive Regression Splines (MARS) using the PLS-SEM framework. The innovation lies in its ability to capture nonlinear and interaction effects between latent variables by leveraging the flexibility of MARS while retaining the latent structure estimation through PLS. The article elaborates the steps of Maximum Likelihood Estimator (MLE) and Ordinary Least Squares (OLS) to estimate values of MARSPLS parameters. The model is evaluated using both simulated and empirical data on e-wallet behavioural intention from 385 Indonesian respondents. Results show that MARSPLS with interaction achieves superior predictive accuracy, as indicated by higher R² value 54.08 % and lower AIC, AICc, and RMSE values. The primary characteristics of the recommended method involve the following:•A novel approach to PLS-SEM that assumes the relationship between latent is nonlinear or unknown.•The model involves four exogenous and one endogenous latent variable, without moderation and mediation effects.