Pemodelan Regresi Robust dengan Estimasi Generalized-M untuk Penanganan Outlier pada Kasus Kusta di Indonesia

  • Linda Purnama Sari Loleh Universitas Negeri Gorontalo
  • Djihad Wungguli Universitas Negeri Gorontalo
  • Muhammad Rezky Friesta Payu Universitas Negeri Gorontalo
  • La Ode Nashar Universitas Negeri Gorontalo
Keywords: leprosy, outliers, robust regression, generalized M-estimation

Abstract

which attacks the skin, peripheral nerves, and other body organs except the central nervous system. New leprosy cases with visible disabilities are classified as Grade 2 disabled leprosy. The number of Grade 2 disabled leprosy cases is an indicator used to show success in early detection of new leprosy cases. However, the leprosy data in Indonesia for 2023 contains outliers that can affect the results of linear regression analysis. To address this issue, this study utilizes the robust regression method of generalized-M estimation, which is an extension of M-estimation. The objectives of this study are to obtain a robust regression model using generalized-M estimation and to identify significantly influential variables. The research findings indicate that these factors have a significant simultaneous impact on the number of leprosy cases with grade 2 disability, and partially, the factor of access to basic sanitation facilities has an influence on the number of leprosy cases with grade 2 disability with an R^2 value of 73%, which can be explained by the predictor variables in this study. Meanwhile, 27% is explained by other predictor variables not included in this study. From these results, it is hoped that the efforts of the government and relevant agencies can improve access to basic sanitation facilities for the prevention and control of leprosy cases in Indonesia.

References

Adityaningrum, A., Resmawan, R., Brahim, A. M., Isa, D. R., Nashar, L. O., & Asriadi, A. (2024). Robust Least Median Of Square Modelling Using Seemingly Unrelated Regression With Generalized Least Square On Panel Data For Tuberculosis Cases. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 18(4), 2293–2306. https://doi.org/10.30598/barekengvol18iss4pp2293-2306

Akolo, I. R., & Nadjamuddin, A. (2022). Analisis Regresi Robust Estimasi Least Trimmed Square dan Estimasi Maximum Likelihood pada Pemodelan IPM di Pulau Sulawesi. Euler : Jurnal Ilmiah Matematika, Sains Dan Teknologi, 10(2), 211–221. https://doi.org/10.34312/euler.v10i2.16708

Aristiarto, R., Susanti, Y., & Susanto, I. (2023). Analisis Regresi Robust Estimasi Gm Pada Indeks Keparahan Kemiskinan Provinsi-Provinsi Di Indonesia. Semnas Ristek (Seminar Nasional Riset Dan Inovasi Teknologi), 7(1). https://doi.org/10.30998/semnasristek.v7i1.6273

Emerson, L. E., Anantharam, P., Yehuala, F. M., Bilcha, K. D., Tesfaye, A. B., & Fairley, J. K. (2020). Poor WASH (Water, Sanitation, and Hygiene) Conditions Are Associated with Leprosy in North Gondar, Ethiopia. International Journal of Environmental Research and Public Health, 17(17), 6061. https://doi.org/10.3390/ijerph17176061

Fitrianto, A., & Xin, S. H. (2022). Comparisons Between Robust Regression Approaches In The Presence Of Outliers And High Leverage Points. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 16(1), 243–252. https://doi.org/10.30598/barekengvol16iss1pp241-250

Gujarati, D. N. (2015). Econometrics by Example. Macmillan Education Palgrave. https://books.google.co.id/books?id=ONpdyQEACAAJ

Kementerian Kesehatan RI. (2024). Profil Kesehatan Indonesia Tahun 2023. https://kemkes.go.id/app_asset/file_content_download/172231123666a86244b83fd8.51637104.pdf

Kurniawan, A., Susanti, Y., & Pratiwi, H. (2023). Pemodelan Produksi Padi di Indonesia Menggunakan Regresi Robust Estimasi Generalized M. Prosiding Seminar Pendidikan Matematika Dan Matematika, 7. https://doi.org/10.21831/pspmm.v7i1.267

Kutner, M. H. (2005). Applied Linear Statistical Models. McGraw-Hill Irwin. https://books.google.co.id/books?id=0xqCAAAACAAJ

Larasati, S. D. A., Nisa, K., & Setiawan, E. (2020). Analisis Regresi Komponen Utama Robust dengan Metode Minimum Covariance Determinant – Least Trimmed Square (MCD-LTS). Jurnal Siger Matematika, 1(1). https://doi.org/10.23960/jsm.v1i1.2472

Maulana, A., Fahdhienie, F., & Ariscasari, P. (2024). Analisis Faktor Yang Berhubungan Dengan Perilaku Masyarakat Dalam Upaya Mencegah Penularan Penyakit Kusta Di Wilayah Kerja Puskesmas Ingin Jaya Kecamatan Aceh Besar Tahun 2023. J-KESMAS: Jurnal Kesehatan Masyarakat, 10(1), 65. https://doi.org/10.35329/jkesmas.v10i1.5068

Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to Linear Regression Analysis (6th ed.). Wiley. https://books.google.co.id/books?id=Y2wYEAAAQBAJ

Montgomery, D. C., & Runger, G. C. (2010). Applied Statistics and Probability for Engineers. John Wiley & Sons. https://books.google.co.id/books?id=_f4KrEcNAfEC

Muamalah, A. F., Ngastiti, P. T. B., & Isro’il, A. (2024). Perbandingan Hasil Model Regresi Robust Estimasi M (Method Of Moment), Estimasi M (Maximum Likelihood Type), Dan Estimasi Lts (Least Trimmed Square) Pada Produksi Padi Di Kecamatan Sekaran. MATHunesa: Jurnal Ilmiah Matematika, 12(3), 540–548. https://ejournal.unesa.ac.id/index.php/mathunesa/article/view/60362

Nabil, F., Susanti, Y., & Zukhronah, E. (2024). Robust Regression Analysis Of Gm Estimation On The Poverty Gap Index Of Indonesian Provinces. Proceeding of International Conference of Religion, Health, Education, Science and Technology, 1(1), 369–374. https://doi.org/10.35316/icorhestech.v1i1.5660

Nugraha, B. (2022). Pengembangan Uji Statistik: Implementasi Metode Regresi Linier Berganda dengan Pertimbangan Uji Asumsi Klasik. Pradina Pustaka. https://books.google.co.id/books?id=PzZZEAAAQBAJ

Prayogo, D., & Sukim, S. (2021). Determinan Daya Beli Masyarakat Indonesia Selama Pandemi Covid-19 Tahun 2020. Seminar Nasional Official Statistics, 2021(1), 631–640. https://doi.org/10.34123/semnasoffstat.v2021i1.987

Rahman, M. I., Nasib, S. K., & Adityaningrum, A. (2025). Robust Minimum Covariance Determinant Scale For Addressing Outliers In Food Security Index Data. Jurnal Riset Dan Aplikasi Matematika (JRAM), 9(1), 77–89. https://journal.unesa.ac.id/index.php/jram/article/view/39061

Rohmah, D., Susanti, Y., & Zukhronah, E. (2020). Perbandingan Model Regresi Robust Estimasi M Dan Estimasi Least Trimmed Squares (LTS) Pada Jumlah Kasus Tuberkulosis Di Indonesia. Kontinu: Jurnal Penelitian Didaktik Matematika, 4(2), 136. https://doi.org/10.30659/kontinu.4.2.136-146

Said, A., Susanti, Y., & Sugiyanto. (2024). Perbandingan Ketepatan Model Regresi Robust Estimasi Method of Moment (MM) dan Estimasi Generalized-M (GM) dalam Memodelkan Harga Penutupan Saham Sektor Teknologi Tahun 2023. SainsMath: Jurnal MIPA Sains Terapan, 3(1), 40–51. https://journal.unindra.ac.id/index.php/sainsmath/article/view/3069

Sari, E. A. R., Hanum Iftitah Firdaus, M Ridwan Winarto, Wahyu Indiyani, Y., & Nooraemi, R. (2018). Perbandingan Regresi OLS dan Robust MM-Estimation Dalam Kasus DBD di Indonesia 2018. Jurnal Education and Development, 8(2), 68–74. https://journal.ipts.ac.id/index.php/ED/article/view/1648

Utomo, A. T., Erfiani, & Fitrianto, A. (2022). Analisis Ridge Robust Penduga Generalized M (GM) Pada Pemodelan Kalibrasi Untuk Kadar Gula Darah. VARIANSI: Journal of Statistics and Its Application on Teaching and Research, 4(2), 59–69. https://jurnalvariansi.unm.ac.id/index.php/variansi/issue/view/2

Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing. Elsevier Science. https://books.google.co.id/books?id=zZ0snCw9aYMC

World Health Organization. (2025). Leprosy. World Health Organization. https://www.who.int/news-room/fact-sheets/detail/leprosy

Wulandari, D. A., Kusnandar, D., & Imro’ah, N. (2022). Estimasi-S Model Regresi Robust Menggunakan Pembobot Welsch Pada Data Indeks Pembangunan Manusia Di Indonesia. Bimaster: Buletin Ilmiah Matematika, Statistika Dan Terapannya, 11(4), 577–586. https://jurnal.untan.ac.id/index.php/jbmstr/article/view/57009/0

Published
2025-09-01