Estimasi Model Regresi Spline Kubik Tersegmen dengan Metode Penalized Least Square
DOI:
https://doi.org/10.24256/jpmipa.v10i2.3197Keywords:
Penalized Least Square, Segmentasi, Spline Kubik.Abstract
Abstract:
Nonparametric regression is used for data whose data pattern is non-parametric. One of the estimators that can be developed is a segmented cubic spline which is able to show several segmentation changes in the data. This article examines the estimation of segmented cubic spline nonparametric regression models using the Penalized Least Square estimation criteria. The method involves knot points and smoothing parameters simultaneously. In addition, the model is used to analyze data on BPJS claims based on patient age. The results show that the optimal model is at two-knot points, namely 26 and 52 with a smoothing parameter of 0.89. There are three segmentation changes from the cubic data, which consist of young people up to 26 years old, 26-52 years old, and 52 years and over.Â
Abstrak:
Regresi nonparametrik digunakan untuk data yang pola datanya bentuk non parametrik. Salah satu estimator yang dapat dikembangkan adalah spline kubik tersegmen yang mampu menunjukkan beberapa segmentasi perubahan pada data. Artikel ini mengkaji estimasi model regresi nonparametrik spline kubik tersegmen melalui kriteria estimasi menggunakan Penalized Least Square. Metode tersebut melibatkan titik knot dan parameter penghalus secara bersamaan. Selain itu, model digunakan untuk menganalisis data klaim BPJS berdasarkan usia pasien. Hasil menunjukkan bahwa model optimal pada dua titik knot yaitu 26 dan 52 dengan parameter penghalus sebesar 0,89. Terdapat tiga segmentasi perubahan data secara kubik, yaitu usia muda hingga 26 tahun, usia 26-52 tahun, dan usia 52 tahun ke atas.Â
References
Aprilia, Bunga, Anna Islamiyati, Anisa Anisa, and Nirwan Ilyas. “Estimasi Model Regresi Kuantil Spline Kuadratik Pada Data Trombosit Dan Hematokrit Pasien DBD.†ESTIMASI: Journal of Statistics and Its Application 1, no. 2 (2020): 58–64. https://doi.org/10.20956/ejsa.v1i2.9264.
Arifin, Samsul, Anna Islamiyati, and Raupong Raupong. “Kemampuan Estimator Spline Linear Dalam Analisis Komponen Utama.†ESTIMASI: Journal of Statistics and Its Application 1, no. 1 (2020): 40–47. https://doi.org/10.20956/ejsa.v1i1.9262.
Budiantara, I. Nyoman, Vita Ratnasari, Madu Ratna, Wahyu Wibowo, Ngizatul Afifah, Dyah Putri Rahmawati, and Made Ayu Dwi Octavanny. “Modeling Percentage of Poor People in Indonesia Using Kernel and Fourier Series Mixed Estimator in Nonparametric Regression.†Investigación Operacional 40, no. 4 (September 5, 2019): 538–50. http://www.invoperacional.uh.cu/index.php/InvOp/article/view/700.
Chamidah, Nur, Kinanti Hanugera Gusti, Eko Tjahjono, and Budi Lestari. “Improving of Classification Accuracy of Cyst and Tumor Using Local Polynomial Estimator.†Telkomnika (Telecommunication Computing Electronics and Control) 17, no. 3 (2019): 1492–1500. https://doi.org/10.12928/TELKOMNIKA.V17I3.12240.
Fernandes, Adji Achmad Rinaldo, I. Nyoman Budiantara, Bambang Widjanarko Otok, and Suhartono. “Spline Estimator for Bi-Responses and Multi-Predictors Nonparametric Regression Model in Case of Longitudinal Data.†Journal of Mathematics and Statistics 11, no. 2 (October 8, 2015): 61–69. https://doi.org/10.3844/jmssp.2015.61.69.
Islamiyati, Anna. “Spline Polynomial Truncated Dalam Regresi Nonparametrik.†Jurnal Matematika, Statistika Dan Komputasi 14, no. 1 (February 11, 2018): 54–60. https://doi.org/10.20956/jmsk.v14i1.3538.
———. “Taksiran Kurva Regresi Spline Pada Data Longitudinal Dengan Kuadrat Terkecil.†Jurnal Matematika, Statistika Dan Komputasi 11, no. 1 (2014): 77–83. https://doi.org/10.20956/jmsk.v11i1.3432.
Islamiyati, Anna, Fatmawati, and Nur Chamidah. “Changes in Blood Glucose 2 Hours After Meals in Type 2 Diabetes Patients Based on Length of Treatment at Hasanuddin University Hospital, Indonesia.†Rawal Medical Journal 45, no. 1 (January 1, 2020): 31–34. http://www.scopus.com/inward/record.url?scp=85081662228&partnerID=8YFLogxK.
———. “Penalized Spline Estimator with Multi Smoothing Parameters in Bi-Response Multi-Predictor Nonparametric Regression Model for Longitudinal Data.†Songklanakarin Journal of Science and Technology 42, no. 4 (2020): 897–909. http://www.scopus.com/inward/record.url?scp=85085869891&partnerID=8YFLogxK.
Lestari, B., Fatmawati, I. N. Budiantara, and N. Chamidah. “Smoothing Parameter Selection Method for Multiresponse Nonparametric Regression Model Using Smoothing Spline and Kernel Estimators Approaches.†Journal of Physics: Conference Series 1397, no. 1 (December 2019): 012064. https://doi.org/10.1088/1742-6596/1397/1/012064.
Mardianto, M. F. F., E. Tjahjono, and M. Rifada. “Semiparametric Regression Based on Three Forms of Trigonometric Function in Fourier Series Estimator.†Journal of Physics: Conference Series 1277, no. 1 (July 2019): 012052. https://doi.org/10.1088/1742-6596/1277/1/012052.
Musafirah, Anna Islamiyati. “Estimation of Penalized Spline Linear Regression Models through Robust M Estimator.†International Journal of Engineering and Information Systems (IJEAIS) 5, no. 11 (November 28, 2021): 166–68. http://ijeais.org/wp-content/uploads/2021/11/abs/IJAAR211120.html.
Puteri, Widya Nauli Amalia, Anna Islamiyati, and Anisa Anisa. “Penggunaan Regresi Kuantil Multivariat Pada Perubahan Trombosit Pasien Demam Berdarah Dengue.†ESTIMASI: Journal of Statistics and Its Application, 2020, 1–9. https://doi.org/10.20956/ejsa.v1i1.9224.
Ramdhani, Zhazha Alifkhamulki, Anna Islamiyati, and Raupong Raupong. “Hubungan Faktor Kolestrol Terhadap Gula Darah Diabetes Dengan Spline Kubik Terbobot.†ESTIMASI: Journal of Statistics and Its Application 1, no. 1 (2020): 32–39. https://doi.org/10.20956/ejsa.v1i1.9252.
Usrah, Muhammad Jayzul, Anna Islamiyati, and Anisa. “Analisis Perubahan Berat Badan Balita Dengan Estimator Penalized Spline Kuadratik.†ESTIMASI: Journal of Statistics and Its Application 3, no. 2 (July 2, 2022): 70–75. https://doi.org/10.20956/ejsa.vi.11459.
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