A Comparative Study of M-Estimation and S-Estimation in Robust Regression Models: A Case Study on Crime Rates in Indonesia
DOI:
https://doi.org/10.24252/msa.v14i1.60365Keywords:
robust, M-estimation, S-estimation, Crime, OutlierAbstract
Robust regression is a regression method used to handle outliers in statistical analysis. Robust regression consists of five estimation methods, namely M-estimation (Maximum Likelihood type), LMS estimation (Least Median of Squares), LTS estimation (Least Trimmed Squares), MM estimation (Method of Moments), and S-estimation (Scale). M-estimation is known for having the smallest variance among the estimators, with high efficiency reaching up to 95%, while S-estimation is based on the residual scale of M-estimation and is characterized by a high breakdown point of up to 50%. The 2022 crime rate data in Indonesia contains outliers. According to data from the Central Statistics Agency, there was a drastic increase in crime incidents in 2022, reaching 372,965 reported cases. Therefore, a comparison of robust regression estimation methods was conducted to obtain the best model that explains the factors influencing crime rates in Indonesia. This study employs robust regression using M-estimation and S-estimation with Tukey bisquare weighting. The dependent variable in this study is the number of crimes in Indonesia in 2022, while the independent variables include population density (x₁), open unemployment rate (x₂), number of poor people (x₃), mean years of schooling/MYS (x₄), and labor force participation rate/TPAK (x₅). The results indicate that S-estimation in robust regression provides the best performance among the methods analyzed.
References
S. Syilfi, D. Ispriyanti, and D. Safitri, “Analisis Regresi Linier Piecewise Dua Segmen,” Jurnal Gaussian, vol. 1, no. 1, pp. 219–228, Oct. 2012.
S. Soemartini, Pencilan (Outlier). Universitas Padjajaran, 2007.
H. Lainun, G. M. Tinungki, and A. Amran, “Perbandingan Penduga M, S, dan MM pada Regresi Linier dalam Menangani Keberadaan Outlier,” Jurnal Matematika Statistika dan Komputasi, vol. 15, no. 1, pp. 88–96, Jul. 2018.
N. Herawati, K. Nisa, and E. Setiawan, “Analisis Ketegaran Regresi Robust Terhadap Letak Pencilan: Studi Perbandingan,” Bulletin of Mathematics, vol. 3, no. 1, pp. 49–60, 2011.
N. A. Atamia, Y. Susanti, and S. S. Handajani, “Perbandingan Analisis Regresi Robust Estimasi-S dan Estimasi-M dengan Pembobot Huber dalam Mengatasi Outlier,” in Prosiding Seminar Nasional Matematika, vol. 4. PRISMA, 2021, pp. 673–679.
C. Chen, “Robust Regression and Outlier Detection with the ROBUSTREG Procedure,” in SUGI Conference Proceedings. SAS Communities, Jan. 2002, pp. 265–278.
A. M. Maziyah, “Penggunaan Regresi Robust Dengan Estimasi-S Dan Estimasi-Mm Dalam Pengembangan Sistem Pendukung Keputusan Guna Memprediksi Tingkat Produksi Padi,” Undergraduate thesis, Institut Teknologi Sepuluh November, 1995.
Z. Setiarini and E. Listyani, “Analisis Regresi Robust Estimasi-S Menggunakan Pembobot Welsch Dan Tukey Bisquare,” Jurnal Matematika, vol. 6, no. 1, pp. 48–55, 2017.
V. J. Yohai, “High Breakdown-Point and High Efficiency Robust Estimates for Regression,” Ann. Statist., vol. 15, no. 2, Jun. 1987.
A. A. Dewayanti and E. Widodo, “Perbandingan Metode Estimasi M Dan Estimasi Mm (Methode Of Moment) pada
Regresi Robust,” in Prosiding Konferensi Nasional Penelitian Matematika dan Pembelajarannya. Surakarta, Indonesia: Program Studi Pendidikan Matematika, Fakultas Keguruan dan Ilmu Pendidikan, Universitas Muhammadiyah Surakarta, Mar. 2016, pp. 751–758.
M. Mardiana, “Perbandingan Model Regresi Robust Estimasi M, Estimasi S dan Estimasi MM pada Faktor yang Mempengaruhi Angka Kejadian Demam Berdarah Dengue di Provinsi Jawa Timur Tahun 2017,” Thesis, Universitas Airlangga, Surabaya, Indonesia, Jun. 2019.
S. Suyono, Analisis Regresi untuk Penelitian. deepublish, Aug. 2015.
H. Ihsan, W. Sanusi, and N. Nurfadillah, “Estimasi Parameter Regresi Linear Pada Kasus Data Outlier Menggunakan
Metode Estimasi Method Of Moment,” JMathCoS, vol. 1, no. 1, p. 38, May 2019.
F. Hidayatulloh, D. Yuniarti, and S. Wahyuningsih, “Regresi Robust dengan Metode Estimasi,” in Prosiding UNINDRA.
Program Studi Teknik Informatika, Fakultas Teknik dan Ilmu Komputer, Universitas Indraprasta PGRI, 2015, pp. 163–170.
A. Widarjono, Ekonometrika: Teori dan Aplikasi untuk Ekonomi dan Bisnis. Yogyakarta Ekonesia, 2007.
T. Tarno, “Estimasi Model Regresi Linier dengan Metode Median Kuadrat Terkecil,” Jurnal Sains & Matematika (JSM), vol. 15, no. 2, pp. 69–72, Apr. 2007.
P. R. Sihombing, S. Suryadiningrat, D. A. Sunarjo, and Y. P. A. C. Yuda, “Identifikasi Data Outlier (Pencilan) dan
Kenormalan Data Pada Data Univariat serta Alternatif Penyelesaiannya,” JESI, vol. 2, no. 3, pp. 307–316, Jan. 2023.
Y. Susanti, H. Pratiwi, S. Sulistijowati H., and T. Liana, “M Estimation, S Estimation, and MM Estimation
in Robust Regression,” Int. J. of Pure and Appl. Math., vol. 91, no. 3, Mar. 2014.
S. Wahyuningsih and D. Yuniarti, “Regresi Robust Linear Sederhana dengan Menggunakan Estimasi MM (Method of
Moment) Simple Linear Regression Robust with MM,” Estimation, vol. 6, pp. 179–186, 2015.
N. R. Draper and H. Smith, Applied Regression Analysis, 1st ed., ser. Wiley Series in Probability and Statistics. Wiley, Apr. 1998.
“Robust Regression,” in Dictionary of Statistics & Methodology. 2455 Teller Road, Thousand Oaks California 91320 United States of America: SAGE Publications, Inc., 2005.
Y. Susanti, S. P. Hasih, and H. Sulistijowati, “Optimasi Model Regresi robust untuk Memprediksi Produksi Kedelai di Indonesia,” in Prosiding Seminar Nasional Matematika dan Pendidikan Matematika. Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Negeri Yogyakarta, Dec. 2013, pp. 253–262.
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