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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi JTAM (Jurnal Teori dan Aplikasi Matematika)
Ullah, Muhammad Ohid
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Mathematics

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Development of Ramsey RESET to Identify the Polynomials Order of Smoothing Spline with Simulation Study Nurdin, Muhammad Rafi Hasan; Fernandes, Adji Achmad Rinaldo; Sumarminingsih, Eni; Ullah, Muhammad Ohid
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.26785

Abstract

Path  analysis is used to determine the effect of exogenous variables on endogenous variables. One of the assumptions in path analysis is the linearity assumption. The linearity assumption can be tested using Ramsey RESET. If the Ramsey RESET results show that all variables are non-linear then one of the alternative models that can be used is nonparametric smoothing spline. The smoothing spline method requires a smoothing spline polynomial order in estimating the nonparametric path analysis function. This polynomial order results in the smoothing spline method having good flexibility in data adjustment. The selection of the smoothing spline polynomial order becomes an obstacle because there is no test to determine the best order. Therefore, the purpose of this study is to find out how the value of V for order 3 and 4, develop Ramsey RESET to identify the best spline polynomial order, and evaluate the Ramsey RESET algorithm through simulation studies on various errors. The results of V values of order 3 and 4 can be obtained through the integral process and it is found that the higher the order, the value of V has a higher rank. Ramsey RESET development is done by modifying the second regression using nonparametric regression functions of order 2, 3, and 4. The simulation study results show that the classical Ramsey RESET can be used to detect linear shapes well because it is not affected by the value of the error variance. However, the classical Ramsey RESET has limitations in detecting non-linear forms other than quadratic and cubic forms so that other forms such as smoothing spline are needed. In testing non-linear models, the lowest p value is obtained in the form that matches the actual conditions, this can be interpreted that the modified Ramsey RESET can detect non-linear forms with spline polynomial orders well. The contribution of this research is to provide a test to identify the best smoothing spline polynomial order using Ramsey RESET modification
Development of Semiparametric Smoothing Spline Path Analysis on Cashless Society Nurdin, Muhammad Rafi Hasan; Ullah, Muhammad Ohid; Fernandes, Adji Achmad Rinaldo; Sumarminingsih, Eni; Solimun, Solimun
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.29846

Abstract

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
Development of Semiparametric Truncated Spline Logistic Path Analysis Rejeki, Sasi Wilujeng Sri; Solimun, Solimun; Nurjannah, Nurjannah; Yulianto, Shalsa Amalia; Ullah, Muhammad Ohid
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.29979

Abstract

Logistic path analysis extends logistic regression by incorporating intervening variables, addressing the limitations of linearity assumptions through nonparametric models like spline regression. However, this study develops a semiparametric truncated spline logistic path analysis to accommodate linear and nonlinear relationships, considering direct and indirect effects of intervening variables. The model is applied to analyze the impact of price volatility and human resource quality on farmer welfare, with farmer productivity as an intervening variable. It assumes a nonlinear relationship between price volatility and productivity/welfare, while other relationships are linear. This development was applied to secondary data collected through questionnaires from farmer group members in Bali Province, which were analyzed using a semiparametric truncated spline logistic path model. Optimal knots were determined using the lowest GCV value. The results show that the model effectively captures changes in data patterns, providing robust parameter estimates. Hypothesis testing highlights significant differences in the effectiveness of linear and nonlinear relationships. The use of truncated splines offers critical insights into variable interactions and enhances model reliability, making it a valuable tool for analyzing complex agricultural systems and informing policies to improve farmer welfare and productivity.
Co-Authors Eni Sumarminingsih Fernandes, Adji Achmad Rinaldo Nurdin, Muhammad Rafi Hasan Nurjannah Nurjannah Rejeki, Sasi Wilujeng Sri Solimun, Solimun Yulianto, Shalsa Amalia