Modified Ramsey RESET in Combined Truncated Spline–Fourier Nonparametric Path Analysis on Waste Management Behavior

Moh Zhafran Hidayatulloh, Solimun Solimun, Adji Achmad Rinaldo Fernandes, Anggun Fadhila Rizqia, Fachira Haneinanda Junianto

Abstract


Nonparametric path analysis is a statistical approach that does not require the functional form of relationships between variables to be known a priori. Classical path analysis assumes linearity, which can be tested using the Ramsey Regression Specification Error Test (RESET). If the linearity test indicates that the relationships between variables are nonlinear, a nonparametric model can be applied. The purpose of this study is to develop a modified Ramsey RESET to identify nonparametric relationships modeled using truncated spline and Fourier series. The modified Ramsey RESET algorithm was successfully implemented to detect the optimal functional form of the nonparametric truncated spline and Fourier series and was subsequently applied to behavioral data on waste management practices. Furthermore, this study proposes an estimator for a hybrid nonparametric path model combining truncated spline and Fourier series approaches. The analysis results reveal that the best model integrates truncated spline with one and two knot points and a Fourier series with one oscillation. The model achieved an adjusted coefficient of determination of 0.956, indicating that it explains 95.6% of the variation in the Behavior of Transforming Waste into Economic Value, while the remaining 4.4% is explained by other unobserved factors outside the model.


Keywords


Fourier Series; Path Analysis; Ramsey RESET; Truncated Spline; Waste Management Behavior

Full Text:

PDF

References


[1] Solimun, Analisis Multivariat Pemodelan Struktural Metode Partial Least Square (PLS). Malang, Indonesia: CV. Citra, 2010.

[2] A. A. R. Fernandes and Solimun, Analisis Regresi dalam Pendekatan Fleksibel: Ilustrasi dengan Paket Program R. Malang, Indonesia: Universitas Brawijaya Press, 2021.

[3] K. A. Yasa, I. N. Suparta, and A. A. N. G. S. Sapteka, “Pemodelan multiple pulse width modulation berbasis fourier series untuk jumlah pulsa sebanyak tiga,” Jurnal Simetrik Politeknik Negeri Madiun, vol. 14, no. 2, 2024. doi: 10.31959/js.v14i2.2669.

[4] L. Laome, I. N. Budiantara, and V. Ratnasari, “Estimation curve of mixed spline trun cated and fourier series estimator for geographically weighted nonparametric regression,” Mathematics, vol. 11, no. 1, p. 152, 2023. doi: 10.3390/math11010152.

[5] A. A. Puspitasari, A. A. R. Fernandes, A. Efendi, S. Astutik, and E. Sumarminingsih, “Development of nonparametric truncated spline at various levels of autocorrelation of longitudinal generating data,” Journal of Statistics Applications and Probability, vol. 12, no. 2, pp. 757–766, 2023.

[6] L. P. Inasari, M. Irwan, W. Abidin, and W. Alwi, “Model regresi nonparametrik dengan pendekatan deret fourier pada kasus tingkat kemiskinan di sulawesi selatan,” Jurnal MSA (Matematika dan Statistika serta Aplikasinya), vol. 12, no. 2, pp. 79–87, 2024.

[7] A. Istiqamah, T. Noor, and P. Sukowati, “Study of household scale waste management in batu city, indonesia: Implementation of batu mayor’s regulation on household waste management policy,” International Journal of Advanced Science Research and Engineering, vol. 8, no. 2, pp. 23–29, 2022.

[8] I. Y. Prastya, “Co-production in waste management through waste banks program in batu city,” Journal of Local Government Issues, vol. 2, no. 2, pp. 149–160, 2024. doi: 10.22219/logos.vol2.no2.149-167.

[9] A. A. R. Fernandes and Solimun, Metode Analisis Data Penelitian: Pendekatan Regresi. Malang, Indonesia: Universitas Brawijaya Press, 2022.

[10] I. Sriliana, I. N. Budiantara, and V. Ratnasari, “A truncated spline and local linear mixed estimator in nonparametric regression for longitudinal data and its application,” Symmetry, vol. 14, no. 12, p. 2687, 2022. doi: 10.3390/sym14122687.

[11] U. Rohma, A. A. R. Fernandes, S. Astutik, and Solimun, “A combined truncated spline and kernel semiparametric path model development,” CAUCHY: Jurnal Matematika Murni dan Aplikasi, vol. 10, no. 1, pp. 82–95, 2025. doi: 10.18860/cauchy.v10i1.29849.

[12] M. F. F. Mardianto, Gunardi, and H. Utami, “An analysis about fourier series estimator in nonparametric regression for longitudinal data,” Mathematics and Statistics, vol. 9, no. 4, pp. 501–510, 2021. doi: 10.13189/ms.2021.090409.

[13] M. W. Ketrin, F. Fitri, A. A. Putra, and Zilrahmi, “Nonparametric regression modeling with fourier series approach on poverty cases in west sumatra province,” UNP Journal of Statistics and Data Science, vol. 1, no. 2, pp. 53–58, 2023. doi: 10.24036/ujsds/vol1-is s2/32.

[14] S. Sifriyani, J. P. Sitinjak, and A. T. R. Dani, “Penerapan model regresi semiparametrik deret fourier untuk mengidentifikasi faktor penentu angka harapan hidup dalam konteks sdgs 3,” Jurnal Gaussian, vol. 14, no. 2, pp. 302–313, 2025. doi: 10.14710/j.gauss.14.2 .302-313.

[15] A. Fitrianto and P. Linganathan, “Comparisons between resampling techniques in linear regression: A simulation study,” CAUCHY: Jurnal Matematika Murni dan Aplikasi, vol. 7, no. 3, pp. 345–353, 2022. doi: 10.18860/ca.v7i3.14550.




DOI: https://doi.org/10.18860/cauchy.v10i2.37239

Refbacks

  • There are currently no refbacks.


Copyright (c) 2025 Moh Zhafran Hidayatulloh, Solimun Solimun, Adji Achmad Rinaldo Fernandes, Anggun Fadhila Rizqia, Fachira Haneinanda Junianto

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.