ROBUST LEAST MEDIAN OF SQUARE MODELLING USING SEEMINGLY UNRELATED REGRESSION WITH GENERALIZED LEAST SQUARE ON PANEL DATA FOR TUBERCULOSIS CASES
Abstract
Tuberculosis, primarily affecting the lungs and other organs, was the leading cause of death worldwide before the COVID-19 pandemic and continues to be a significant health concern. This research examined tuberculosis (TB) using a panel dataset. As a consequence, the datasets may contain outliers and contemporaneous correlations. A Robust Least Median of Square (LMS) model was developed in this research by combining Seemingly Unrelated Regression (SUR) with Generalized Least Square (GLS) on panel data to provide an analysis overview to overcome outliers and contemporaneous correlations. Based on secondary data obtained from the Central Bureau of Statistics of the Gorontalo Province and the Ministry of Health of the Gorontalo Province, this research examines TB cases between 2017 and 2021. The Chow test result suggests that CEM is the most appropriate model for analyzing panel data for TB cases in Gorontalo Province between 2017 and 2021. Due to the presence of outliers and influential observations in the data, robust LMS is employed. Furthermore, there is a problem of contemporaneous correlation in this research. Each regency or city can mitigate this problem by implementing robust LMS using SUR with GLS.
Downloads
References
H. Jusuf, M. Sakti, I. Husein, M. Elveny, R. Syah, and S. Tuba, “Modelling Optimally to the Treatment of TB Patients for Increase Medical Knowledge,” Syst. Rev. Pharm., vol. 11, no. 4, pp. 742–748, 2020, [Online]. Available: https://www.sysrevpharm.org/articles/modelling-optimally-to-the-treatment-of-tb-patients-for-increase-medical-knowledge.pdf
S. S. Rajak, S. Ismail, and R. Resmawan, “Metode Conditional Autoregressive dalam Analisis Penyebaran Kasus Penyakit Tuberculosis,” Jambura J. Probab. Stat., vol. 2, no. 1, pp. 28–34, Apr. 2021, doi: 10.34312/jjps.v2i1.9771.
WHO, Global Tuberculosis Report 2022. WHO, 2022.
Dinas Kesehatan Provinsi Gorontalo, “Profil Kesehatan 2021.” Dinas Kesehatan Provinsi Gorontalo, 2021.
D. N. Gujarati, Econometrics by Example. Macmillan Education Palgrave, 2015. [Online]. Available: https://books.google.co.id/books?id=ONpdyQEACAAJ
M. Irwansyah, R. Ruliana, and M. K. Aidid, “Analisis Regresi Balanced Panel dengan Komponen Galat Dua Arah pada Kasus Melek Huruf Masyarakat di Provinsi NTB,” VARIANSI J. Stat. Its Appl. Teach. Res., vol. 3, no. 1, p. 10, Mar. 2021, doi: 10.35580/variansiunm14644.
A. Kustanto, “The role of socioeconomic and environmental factors on the number of tuberculosis cases in Indonesia,” J. Ekon. Pembang., vol. 18, no. 2, pp. 129–146, Dec. 2020, doi: 10.29259/jep.v18i2.12553.
E. D. Sihaloho, I. L. Alfarizy, and E. B. Sagala, “Indikator Ekonomi dan Angka Tuberkulosis di Kabupaten Kota di Jawa Barat,” J. Ilmu Ekon. dan Pembang., vol. 19, no. 2, pp. 128–138, 2019, [Online]. Available: https://jurnal.uns.ac.id/jiep/article/view/33698
D. Suliyanto, Ekonometrika Terapan: Teori dan Aplikasi dengan SPSS, 1st ed. Yogyakarta: Andi, 2011. [Online]. Available: https://scholar.google.com/scholar?cluster=3601403273910001182&hl=en&oi=scholarr
I. Alamsyah, R. Esra, S. Awalia, and D. Nohe, “Analisis Regresi Data Panel untuk Mengetahui Faktor yang Memengaruhi Jumlah Penduduk Miskin di Kalimantan Timur,” Pros. Semin. Nas. Mat. dan Stat., vol. 2, 2022, [Online]. Available: http://jurnal.fmipa.unmul.ac.id/index.php/SNMSA/article/view/861
C. O. Arimie, E. O. Biu, and M. A. Ijomah, “Outlier Detection and Effects on Modeling,” OALib, vol. 07, no. 09, pp. 1–30, 2020, doi: 10.4236/oalib.1106619.
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, Oct. 2019, doi: 10.30598/barekengvol13iss3pp145-156ar884.
H. Khotimah and Suwanda, “Pemodelan Quantile Regression untuk Menentukan Faktor-Faktor Penyebab Penyakit Tuberkulosis Paru di Kabupaten Tasikmalaya,” Bandung Conf. Ser. Stat., vol. 2, no. 2, pp. 61–70, Jul. 2022, doi: 10.29313/bcss.v2i2.3068.
C. S. K. Dash, A. K. Behera, S. Dehuri, and A. Ghosh, “An outliers detection and elimination framework in classification task of data mining,” Decis. Anal. J., vol. 6, p. 100164, Mar. 2023, doi: 10.1016/j.dajour.2023.100164.
H. Sugiarti and A. Megawarni, “Tingkat efisiensi penaksir M terhadap penaksir LMS dalam menaksir koefisien garis regresi,” J. Mat. Sains dan Teknol., vol. 11, no. 2, pp. 90–98, 2010.
D. Rohmah, Y. Susanti, and E. Zukhronah, “Perbandingan Model Regresi Robust Estimasi M dan Estimasi Least Trimmed Squares (LTS) pada Jumlah Kasus Tuberkulosis di Indonesia,” Kontinu J. Penelit. Didakt. Mat., vol. 4, no. 2, p. 136, Nov. 2020, doi: 10.30659/kontinu.4.2.136-146.
S. Heritier, E. Cantoni, S. Copt, and M.-P. Victoria-Feser, Robust Methods in Biostatistics. Germany: Wiley, 2009. [Online]. Available: https://scholar.google.com/scholar?cluster=4506501391474728644&hl=en&as_sdt=0,5
H. Riazoshams, H. Midi, and G. Ghilagaber, Robust Nonlinear Regression: with Applications using R. United Kingdom: Wiley, 2018. [Online]. Available: https://scholar.google.com/scholar?oi=bibs&hl=en&cluster=18421333600214340159
L. S. Febrianto, P. Hendikawati, and N. K. Dwidayati, “Perbandingan Metode Robust Least Median of Square (LMS) dan Penduga S Untuk Menangani Outlier Pada Regresi Linier Berganda,” Unnes J. Math., vol. 7, no. 1, pp. 83–95, 2018.
K. Khotimah, K. Sadik, and A. Rizki, “Study of Robust Regression Modeling Using MM-Estimator and Least Median Squares,” 2019. doi: 10.4108/eai.2-8-2019.2290533.
W. Jannah, I. D. Sulvianti, Indahwati, P. Silvianti, and A. Kurnia, “Analysis of Credit Bank Distribution with Seemingly Unrelated Regression Method on Panel Data,” J. Phys. Conf. Ser., vol. 1863, no. 1, p. 012057, Mar. 2021, doi: 10.1088/1742-6596/1863/1/012057.
D. A. Yulianto, S. Sugiman, and A. Agoestanto, “Estimasi Parameter Regresi Robust Model Seemingly Unrelated Regrssion (SUR) dengan Metode Generalized Least Square (GLS),” Unnes J. Math., vol. 7, no. 2, pp. 216–227, 2018, doi: https://doi.org/10.15294/ujm.v7i2.21463.
A. Widyaningsih, M. Susilawati, and I. W. Sumarjaya, “Estimasi Model Seemingly Unrelated Regression (SUR) dengan Metode Generalized Least Square (GLS),” J. Mat., vol. 4, no. 2, pp. 102–110, 2014, [Online]. Available: https://ojs.unud.ac.id/index.php/jmat/article/view/12554
K. Peremans and S. Van Aelst, “Robust Inference for Seemingly Unrelated Regression Models,” J. Multivar. Anal., vol. 167, pp. 212–224, Sep. 2018, doi: 10.1016/j.jmva.2018.05.002.
A. Fitriana, W. Pramesti, and E. M. P. Hermanto, “Pemodelan Seemingly Unrelated Regression (SUR) pada Faktor Pertumbuhan Perekonomian di Provinsi Jawa Timur Tahun 2018,” J Stat. J. Ilm. Teor. dan Apl. Stat., vol. 13, no. 2, pp. 12–19, Dec. 2020, doi: 10.36456/jstat.vol13.no2.a2950.
A. Anisa, “Seemingly Unrelated Regression (SUR) Penderita Penyakit DBD RS. Wahidin Sudirohusodo Dan RS. Stella Maris Makassar,” J. Mat. Stat. dan Komputasi, vol. 13, no. 1, pp. 20–25, 2016, [Online]. Available: https://journal.unhas.ac.id/index.php/jmsk/article/view/3475
A. G. Ghazal and S. A. Hegazy, “The two feasible seemingly unrelated regression estimator,” Int. J. Sci. Technol. Res., vol. 4, no. 4, pp. 247–253, 2015, [Online]. Available: https://www.ijstr.org/final-print/apr2015/The-Two-Feasible-Seemingly-Unrelated-Regression-Estimator.pdf
A. Y. Kartini, N. Cahyani, and N. Himawati, “Regresi Data Panel untuk Pemodelan Jumlah Penderita Tuberculosis di Kabupaten Bojonegoro,” J. Stat. dan Apl., vol. 6, no. 2, pp. 264–275, Dec. 2022, doi: 10.21009/JSA.06212.
A. R. Widyaningrum, Y. Susanti, and I. Slamet, “Pemodelan Penyakit Diare Balita di Jawa Timur Menggunakan Regresi Robust,” in SINASIS (Seminar Nasional Sains), 2021, vol. 2, no. 1. [Online]. Available: https://proceeding.unindra.ac.id/index.php/sinasis/article/view/5393
M. Kurniati, Y. Yundari, and S. W. Rizki, “Metode Least Median Square (LMS) dalam Analisis Regresi Robust Ketika Terdapat Outlier,” Bimaster Bul. Ilm. Mat. Stat. dan Ter., vol. 8, no. 4, Oct. 2019, doi: 10.26418/bbimst.v8i4.36553.
T. Tusilowati, L. Handayani, and R. Rais, “Simulasi Penanganan Pencilan pada Analisis Regresi Menggunakan Metode Least Median Square (LMS),” J. Ilm. Mat. DAN Terap., vol. 15, no. 2, pp. 238–247, 2018.
P. J. Rousseeuw, “Least Median of Squares Regression,” J. Am. Stat. Assoc., vol. 79, no. 388, p. 871, Dec. 1984, doi: 10.2307/2288718.
M. Bilodeau and P. Duchesne, “Robust estimation of the SUR model,” Can. J. Stat., vol. 28, no. 2, pp. 277–288, Jun. 2000, doi: 10.2307/3315978.
J.-M. Dufour and L. Khalaf, “Exact tests for contemporaneous correlation of disturbances in seemingly unrelated regressions,” J. Econom., vol. 106, no. 1, pp. 143–170, Jan. 2002, doi: 10.1016/S0304-4076(01)00093-8.
D. N. Gujarati and D. C. Porter, Basic Econometrics, 5th ed. McGraw-Hill Education, 2008. [Online]. Available: https://books.google.co.id/books?id=zJlDPgAACAAJ
I. R. Akolo and A. Nadjamuddin, “Analisis Regresi Robust Estimasi Least Trimmed Square dan Estimasi Maximum Likelihood pada Pemodelan IPM di Pulau Sulawesi,” Euler J. Ilm. Mat. Sains dan Teknol., vol. 10, no. 2, pp. 211–221, Oct. 2022, doi: 10.34312/euler.v10i2.16708.
B. H. Baltagi, Econometric Analysis of Panel Data. United Kingdom: Wiley, 2005. [Online]. Available: https://books.google.co.id/books?id=31ruAAAAMAAJ
M. J. Hidayat, A. F. Hadi, and D. Anggraeni, “Analisis Regresi Data Panel Terhadap Indeks Pembangunan Manusia (IPM) Jawa Timur Tahun 2006-2015,” Maj. Ilm. Mat. dan Stat., vol. 18, no. 2, p. 69, Sep. 2018, doi: 10.19184/mims.v18i2.17250.
D. A. Wulandari, D. Kusnandar, and N. Imro’ah, “Estimasi-S Model Regresi Robust menggunakan Pembobot Welsch pada Data Indeks Pembangunan Manusia di Indonesia,” Bimaster Bul. Ilm. Mat. Stat. dan Ter., vol. 11, no. 4, 2022, [Online]. Available: https://jurnal.untan.ac.id/index.php/jbmstr/article/view/57009
H. W. Lilliefors, “On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown,” J. Am. Stat. Assoc., vol. 62, no. 318, p. 399, Jun. 1967, doi: 10.2307/2283970.
G.- MARDIATMOKO, “PENTINGNYA UJI ASUMSI KLASIK PADA ANALISIS REGRESI LINIER BERGANDA,” BAREKENG J. Ilmu Mat. dan Terap., vol. 14, no. 3, pp. 333–342, Oct. 2020, doi: 10.30598/barekengvol14iss3pp333-342.
A. Adityaningrum, N. Arsad, and H. Jusuf, “Faktor Penyebab Stunting di Indonesia: Analisis Data Sekunder Data SSGI Tahun 2021,” Jambura J. Epidemiol., vol. 2, no. 1, pp. 1–10, 2023, [Online]. Available: https://ejurnal.ung.ac.id/index.php/jje/article/view/21542
T. Tuwanakotta, M. W. Talakua, Y. W. A. Nanlohy, and L. J. Sinay, “PENERAPAN REGRESI DATA PANEL UNTUK MEMODELKAN APBD DI PROVINSI MALUKU,” Var. J. Stat. Its Appl., vol. 2, no. 1, pp. 15–26, Jul. 2020, doi: 10.30598/variancevol2iss1page15-26.
N. Shrestha, “Detecting Multicollinearity in Regression Analysis,” Am. J. Appl. Math. Stat., vol. 8, no. 2, pp. 39–42, Jun. 2020, doi: 10.12691/ajams-8-2-1.
Copyright (c) 2024 Amanda Adityaningrum, Resmawan Resmawan, Annisa Maharani Brahim, Dewi Rahmawaty Isa, La Ode Nashar, Asriadi Asriadi
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this Journal agree to the following terms:
- Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
- Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
- Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.
1.gif)
