Estimasi Model Regresi Spline Kubik Tersegmen dengan Metode Penalized Least Square

Authors

  • Anna Islamiyati Universitas Hasanuddin, Indonesia https://orcid.org/0000-0001-6441-0306
  • Anisa Anisa Universitas Hasanuddin, Indonesia
  • Raupong Raupong Universitas Hasanuddin
  • Jusmawati Massalesse Universitas Hasanuddin, Indonesia
  • Nasrah Sirajang Universitas Hasanuddin, Indonesia
  • Sitti Sahriman Universitas Hasanuddin, Indonesia
  • Alfiana Wahyuni Universitas Hasanuddin, Indonesia

DOI:

https://doi.org/10.24256/jpmipa.v10i2.3197

Keywords:

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. 

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. 

Author Biographies

Anna Islamiyati, Universitas Hasanuddin

Departemen Statistika

Anisa Anisa, Universitas Hasanuddin

Departemen Statistika

Raupong Raupong, Universitas Hasanuddin

Departemen Statistika

Jusmawati Massalesse, Universitas Hasanuddin

Departemen Matematika

Nasrah Sirajang, Universitas Hasanuddin

Departemen Statistika

Sitti Sahriman, Universitas Hasanuddin

Departemen Statistika

Alfiana Wahyuni, Universitas Hasanuddin

Departemen Statistika

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Published

23-10-2022

How to Cite

Islamiyati, A., Anisa, A., Raupong, R., Massalesse, J., Sirajang, N., Sahriman, S., & Wahyuni, A. (2022). Estimasi Model Regresi Spline Kubik Tersegmen dengan Metode Penalized Least Square. Al-Khwarizmi : Jurnal Pendidikan Matematika Dan Ilmu Pengetahuan Alam, 10(2), 139–148. https://doi.org/10.24256/jpmipa.v10i2.3197

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