COMPARISON OF ROBUST ESTIMATION ON MULTIPLE REGRESSION MODEL
Abstract
This study aimed to compare the robustness of the OLS method with a robust regression model on data that had outliers. The methods used on the robust regression model were M-estimation, MM-estimation, and S-estimation. The step taken was to check the characteristics of the data against outliers. Furthermore, the data were modeled with and without outliers using the OLS method and the M-, MM-, and S-estimations. The results were very different between the data with and without the outlier models in the OLS method. It was reflected in the intercept and standard error variables generated from the models. Meanwhile, the regression model with the M-, MM-, and S-estimations was quite stable and able to withstand the presence of outliers. Based on the three estimations that were robust against the outliers, the MM-estimation was the best candidate because, in addition to having a stable intercept parameter estimation, it also had the smallest standard error, which was 61.9 in the resulting model.
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References
W. Wilsen, W. Rahayu, and V. M. Santi, “Penerapan Imputasi Ganda dengan Metode Predictive Mean Matching (PMM) untuk Pendugaan Data Hilang pada Model Regresi Linear,” J. Stat. dan Apl., vol. 2, no. 1, pp. 12–20, 2018, doi: 10.21009/jsa.02102.
M. B. Rahman and E. Widodo, “Perbandingan Metode Regresi Robust Estimasi Least Trimmed Square , Estimasi Scale , dan Estimasi Method Of Moment,” in Prosiding Seminar Nasional Matematika, 2018, vol. 1, pp. 426–433. [Online]. Available: https://journal.unnes.ac.id/sju/index.php/prisma/article/view/19689
A. T. Tholaby MS and A. Djunaidy, “Untuk Memperbaiki Kinerja Fuzzy Time Series Pada Peramalan Harga Saham Bursa Efek,” J. Ilm. Mikrotek, vol. 2, no. 4, 2017.
G. S. Na, D. Kim, and H. Yu, “DILOF: Effective and memory efficient local outlier detection in data streams,” Proc. ACM SIGKDD Int. Conf. Knowl. Discov. Data Min., pp. 1993–2002, 2018, doi: 10.1145/3219819.3220022.
S. Indra, D. Vionanda, and R. Sriningsih, “Pendeteksian Data Pencilan dan Pengamatan Berpengaruh pada Beberapa Kasus Data Menggunakan Metode Diagnostik,” UNP J. Math., vol. 1, no. 2, pp. 67–74, 2013, [Online]. Available: http://ejournal.unp.ac.id/students/index.php/mat/article/view/1265/942
C. Chen and L.-M. Liu, “Joint Estimation of Model Parameters and Outlier Effects in Time Series,” J. Am. Stat. Assoc., vol. 88, no. 421, pp. 284–297, 1993, doi: 10.1080/01621459.1993.10594321.
S. Candraningtyas, D. Safitri, and D. Ispriyanti, “Regresi Robust MM-Estimator Untuk Penanganan Pencilan Pada Regresi Linier Berganda,” J. Gaussian, vol. 2, no. 4, pp. 395–404, 2013, doi: https://doi.org/10.14710/j.gauss.v2i4.3806.
Z. A. Bakar, R. Mohemad, A. Ahmad, and M. M. Deris, “A comparative study for outlier detection techniques in data mining,” in 2006 IEEE Conference on Cybernetics and Intelligent Systems, 2006, pp. 1–6. doi: 10.1109/ICCIS.2006.252287.
J. A. S. Almeida, L. M. S. Barbosa, A. A. C. C. Pais, and S. J. Formosinho, “Improving hierarchical cluster analysis: A new method with outlier detection and automatic clustering,” Chemom. Intell. Lab. Syst., vol. 87, no. 2, pp. 208–217, 2007, doi: 10.1016/j.chemolab.2007.01.005.
A. Shodiqin, A. N. Aini, and M. R. Rubowo, “Perbanding Dua Metode Regresi Robust yakni Metode Least Trimmed Squares (LTS) dengan metode Estimator-MM (Estmasi-MM) (Studi Kasus Data Ujian Tulis Masuk Terhadap Hasil IPK Mahasiswa UPGRIS),” J. Ilm. Teknosains, vol. 4, no. 1, p. 35, 2018, doi: 10.26877/jitek.v4i1.2403.
A. S. Hadi and J. S. Simonoff, “Procedures for the identification of multiple outliers in linear models,” J. Am. Stat. Assoc., vol. 88, no. 424, pp. 1264–1272, 1993, doi: 10.1080/01621459.1993.10476407.
G. Barbato, E. M. Barini, G. Genta, and R. Levi, “Features and performance of some outlier detection methods,” J. Appl. Stat., vol. 38, no. 10, pp. 2133–2149, 2011, doi: 10.1080/02664763.2010.545119.
L. C. Chang, D. K. Jones, and C. Pierpaoli, “RESTORE: Robust estimation of tensors by outlier rejection,” Magn. Reson. Med., vol. 53, no. 5, pp. 1088–1095, 2005, doi: 10.1002/mrm.20426.
N. A. Atamia, Y. Susanti, and S. S. Handajani, “Analisis Perbandingan Regresi Robust EstimasiI-M Huber dan Estimasi-S dalam Mengatasi Outlier,” in PRISMA, Prosiding Seminar Nasional Matematika, 2015, vol. 4, pp. 673–679.
S. Sunaryo and T. H. Siagian, “Mengatasi Masalah Multikolinearitas Dan Outlier Dengan Pendekatan Robpca,” J. Mat. Saint dan Teknol., vol. 12, no. 1, pp. 1–10, 2011.
G. A. M. Srinadi, “Pengaruh Outlier Terhadap Estimator Parameter Regresi dan Metode Regresi Robust,” Pros. Konf. Nas. Mat. XVII - 2014, no. June 2014, pp. 1259–1266, 2014.
A. R. Fadilah, A. Fitrianto, and I. M. Sumertajaya, “OUTLIER IDENTIFICATION ON PENALIZED SPLINE REGRESSION MODELING FOR POVERTY GAP INDEX IN JAVA,” vol. 16, no. 4, pp. 1231–1240, 2022.
Y. Susanti, H. Pratiwi, H. Sulistijowati, and T. Liana, “M Estimation, s estimation, and mm estimation in robust regression,” Int. J. Pure Appl. Math., vol. 91, no. 3, pp. 349–360, 2014, doi: 10.12732/ijpam.v91i3.7.
D. Cahyawati, H. Tabuji, and R. Abdiati, “Efektivitas Metode Regresi Robust Penduga Welsch dalam Mengatasi Pencilan pada Pemodelan Regresi Linear Berganda,” J. Penelit. Sains, vol. 12, no. 1, pp. 1–7, 2009, doi: https://doi.org/10.26554/jps.v12i1.182.
D. Blatná, “Application of Robust Regression and Bootstrap in Productivity Analysis of GERD Variable in EU27,” Stat. Stat. Econ. J., vol. Vol. 94, no. 2, pp. 62–76, 2014, [Online]. Available: https://pdfs.semanticscholar.org/d648/592c98bc63164ac6f6989e1af5c525a06817.pdf
P. J. Rousseeuw and M. Hubert, “Robust statistics for outlier detection,” Wiley Interdiscip. Rev. Data Min. Knowl. Discov., vol. 1, no. 1, pp. 73–79, 2011, doi: 10.1002/widm.2.
C. Chen, “Robust Regression and Outlier Detection with the ROBUSTREG Procedure,” in SAS Institute Inc., 2002, pp. 265–27.
A. Semar, F. Virgantari, and H. Wijayanti, “Perbandingan Estimasi S (Scale) Dan Estimasi Mm (Method of Moment) Pada Model Regresi Robust Dengan Data Pencilan,” Statmat J. Stat. Dan Mat., vol. 2, no. 1, p. 21, 2020, doi: 10.32493/sm.v2i1.4207.
J. Ha, S. Seok, and J. S. Lee, “A precise ranking method for outlier detection,” Inf. Sci. (Ny)., vol. 324, pp. 88–107, 2015, doi: 10.1016/j.ins.2015.06.030.
A. A.-F. N. Wahyudin, A. Primajaya, and A. S. Y. Irawan, “Penerapan Algoritma Regresi Linear Berganda Pada Estimasi Penjualan Mobil Astra Isuzu,” Techno.Com, vol. 19, no. 4, pp. 364–374, 2020, doi: 10.33633/tc.v19i4.3834.
J. Grosz, “Identification of Influential Points in a Linear Regression Model,” Stat. Stat. Econ. J., vol. 48, no. 1, pp. 71–77, 2011.
D. C. Montgomery, P. E. A., and G. G. Vining, Introduction To Linear Regression Analysis, 5nd Edition. New York: John Wiley & Sons, Inc., 2006.
L. J. Sinay and M. W. Talakua, “Pemodelan Harga Saham Indeks Lq45 Menggunakan Regresi Linier Robust M-Estimator: Huber Dan Bisquare,” BAREKENG J. Ilmu Mat. dan Terap., vol. 9, no. 1, pp. 51–61, 2014, doi: 10.30598/barekengvol9iss1pp51-61.
D. Q. F. de Menezes, D. M. Prata, A. R. Secchi, and J. C. Pinto, “A review on robust M-estimators for regression analysis,” Comput. Chem. Eng., vol. 147, p. 107254, 2021, doi: 10.1016/j.compchemeng.2021.107254.
A. Z. S. W. R. Hendra Perdana, “Analisis Regresi Robust Estimasi-Mm Dalam Mengatasi Pencilan Pada Regresi Linear Berganda,” Bimaster Bul. Ilm. Mat. Stat. dan Ter., vol. 9, no. 1, pp. 123–128, 2020, doi: 10.26418/bbimst.v9i1.38666.
V. J. Yohai, High Breakdown Point and High Efficiency Robust Estimates for Regression. Annals of Statistics, 1987.
C. Leys, O. Klein, Y. Dominicy, and C. Ley, “Detecting multivariate outliers: Use a robust variant of the Mahalanobis distance,” J. Exp. Soc. Psychol., vol. 74, no. September 2017, pp. 150–156, 2018, doi: 10.1016/j.jesp.2017.09.011.
M. A. Nahdliyah, T. Widiharih, and A. Prahutama, “Metode K-Medoids Clustering dengan Validasi Silhouette Index dan C-Index,” J. Gaussian, vol. 8, no. 2, pp. 161–170, 2019.
I. F. Maharani, N. Satyahadewi, and D. Kusnandar, “Metode Ordinary Least Squares Dan Least Trimmed Squares Dalam Mengestimasi Parameter Regresi Ketika Terdapat Outlier,” Bul. Ilm. Mat. Stat. dan Ter., vol. 03, no. 3, pp. 163–168, 2014, doi: http://dx.doi.org/10.26418/bbimst.v3i03.7350.
F. Daniel, “Mengatasi Pencilan Pada Pemodelan Regresi Linear Berganda Dengan Metode Regresi Robust Penaksir Lms,” BAREKENG J. Ilmu Mat. dan Terap., vol. 13, no. 3, pp. 145–156, 2019, doi: 10.30598/barekengvol13iss3pp145-156ar884.
A. Fitrianto and S. H. Xin, “Comparisons Between Robust Regression Approaches in the Presence of Outliers and High Leverage Points,” BAREKENG J. Ilmu Mat. dan Terap., vol. 16, no. 1, pp. 243–252, 2022, doi: 10.30598/barekengvol16iss1pp241-250.
A. D. Deria, A. Hoyyi, and M. Mustafid, “Regresi Robust Estimasi-M Dengan Pembobot Andrew, Pembobot Ramsay Dan Pembobot Welsch Menggunakan Software R,” J. Gaussian, vol. 8, no. 3, pp. 377–388, 2019, doi: 10.14710/j.gauss.v8i3.26682.
N. Nurdin, Raupong, and A. Islamiyati, “Penggunaan Regresi Robust Pada Data Yang Mengandung Pencilan Dengan Metode Momen,” Mat. Stat. dan Komputasi, vol. 10, no. 2, p. 115, 2014, [Online]. Available: http://journal.unhas.ac.id/index.php/jmsk/article/download/3418/1955
R. Finger, “Investigating the performance of different estimation techniques for crop yield data analysis in crop insurance applications,” Agric. Econ. (United Kingdom), vol. 44, no. 2, pp. 217–230, 2013, doi: 10.1111/agec.12005.
J. W. Wisnowski, D. C. Montgomery, and J. R. Simpson, “A comparative analysis of multiple outlier detection procedures in the linear regression model,” Comput. Stat. Data Anal., vol. 36, no. 3, pp. 351–382, 2001, doi: 10.1016/S0167-9473(00)00042-6.
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