Development of Ramsey RESET to Identify the Polynomials Order of Smoothing Spline with Simulation Study

Muhammad Rafi Hasan Nurdin; Adji Achmad Rinaldo Fernandes; Eni Sumarminingsih; Muhammad Ohid Ullah

doi:10.31764/jtam.v9i1.26785

Development of Ramsey RESET to Identify the Polynomials Order of Smoothing Spline with Simulation Study

Muhammad Rafi Hasan Nurdin, Adji Achmad Rinaldo Fernandes, Eni Sumarminingsih, Muhammad Ohid Ullah

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

Keywords

Nonparametric Path; Smoothing Spline; Polynomial Order; Simulation Study.

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DOI: https://doi.org/10.31764/jtam.v9i1.26785