Development of Semiparametric Smoothing Spline Path Analysis on Cashless Society - Muhammad Rafi Hasan Nurdin; Muhammad Ohid Ullah; Adji Achmad Rinaldo Fernandes; Eni Sumarminingsih; Solimun Solimun (CAUCHY: Jurnal Matematika Murni dan Aplikasi, 2025)
Path analysis requires assumptions to be met, particularly the linearity assumption, which can be tested using the Ramsey Regression Specification Error Test (RESET). Parametric path analysis is appropriate when all variable relationships are linear. For entirely non-linear relationships, a nonparametric model can be used, while a semiparametric model applies if there is a mix of linear and non-linear relationships. One nonparametric method is spline smoothing, which requires determining the spline polynomial order in estimating the nonparametric path function. Determining the spline polynomial order is challenging because there is no standard test for it. This study thus develops a modified Ramsey RESET to identify the optimal spline smoothing order. The development involves modifying the second regression equation with a nonparametric spline smoothing regression of orders 2 to 5. The modified Ramsey RESET algorithm is applied to cashless data, and the results are used to estimate a multi-group semiparametric smoothing spline function with a dummy variable approach. This estimation yields a goodness of fit of 94.14%, indicating that Product Quality and the Moderating Effect of Cashless Usage Frequency can explain Cashless User Satisfaction and Cashless User Loyalty by 94.14%, with the remaining 5.86% explained by variables outside the research model