Article Sidebar

Submitted
January 12, 2023
Accepted
January 13, 2023
Published
January 16, 2023
Download
PDF
Statistic
Read Counter : 657 Download : 587

Main Article Content

Abstract

Regression analysis is a method used to determine the relationship between one dependent variable and one or more independent variables. However, the existence of outliers in the 2018 Community Literacy Development Index data led to the application of statistical methods not sensitive to pencils for analysis. This was the reason for adopting robust regression methods, including the M, S, and MM estimations. Therefore, this research aims to compare these three estimates and select the one with the best estimate based on the parameter estimation model associated with the RSE and R2 values. Descriptive and inferential analysis with robust regression was used due to several outlier data and to provide good regression model results with unbiased values. It was discovered that the S-estimator and MM-estimator are the best methods because they have the most minor Residual Standard Error (RSE) of 1.856 and R2 of 0.9778.

Keywords

robust regression anaysis Outliers estimators literacy index

Article Details

License

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
How to Cite
Rahayu, D. A., Nursholihah, U. F., Suryaputra, G., & Surono, S. (2023). Comparasion of The M, MM and S Estimator in Robust Regression Analysis on Indonesian Literacy Index Data 2018. EKSAKTA: Journal of Sciences and Data Analysis, 4(1), 11–22. https://doi.org/10.20885/EKSAKTA.vol4.iss1.art2
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

References

  1. Z. Aflakhah, J. Jajang, and A. T. Br. Sb., Kajian Metode Ordinary Least Square Dan Robust Estimasi M Pada Model Regresi Linier Sederhana Yang Memuat Outlier, J. Ilm. Mat. dan Pendidik. Mat., 11(1) (2020).
  2. D. Alita, A. D. Putra, and D. Darwis, Analysis of classic assumption test and multiple linear regression coefficient test for employee structural office recommendation, Indonesian J. Comput. Cybern. Syst., 15(3) (2021) 295.
  3. Y. Bee Wah and N. Mohd Razali, Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling tests, J. Stat. Model. Anal., 2(11) (2011) 21–33.
  4. A. F. Schmidt and C. Finan, Linear regression and the normality assumption, J. Clin. Epidemiol., 98 (2018) 146–151.
  5. S. Hadi, A. S., and Chatterjee, Regression analysis by example. John Wiley & Sons., 2015.
  6. M. Williams, C. A. Gomez Grajales, and D. Kurkiewicz, Assumptions of Multiple Regression: Correcting Two Misconceptions - Practical Assessment, Research & Evaluation, Evaluación práctica, Investig. y evaluación, 18(11) (2013) 1–16.
  7. O. Ayinde, K., Lukman, A. F., and Arowolo, Robust regression diagnostics of influential observations in linear regression model, Open J. Stat., 5(4) (2015) 273.
  8. C. L. Su, X., and Tsai, Outlier detection, Wiley Interdiscip. Rev. Data Min. Knowl. Discov., 1(3) (2011) 261–268.
  9. C. Yu and W. Yao, Robust linear regression: A review and comparison, Commun. Stat. Simul. Comput., 46(8) (2017) 6261–6282.
  10. R. P. Flora, D. B., LaBrish, C., & Chalmers, Old and new ideas for data screening and assumption testing for exploratory and confirmatory factor analysis. , Front. Psychol., 2(55) (2012).
  11. Ö. G. Alma, Comparison of Robust Regression Methods in Linear Regression, Int. J. Contemp. Math. Sci., 6(9) (2011) 409–421.
  12. D. Huang, R. Cabral, and F. Dela Torre, Robust Regression, IEEE Trans. Pattern Anal. Mach. Intell., 38(2) (2016) 363–375.
  13. G. G. Montgomery, D. C., Peck, E. A., and Vining, Introduction to linear regression analysis. John Wiley & Sons., 2021.
  14. 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., 2(1) (2020) 21.
  15. 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, 4(1) (2018) 35–42.
  16. R. V Hogg and A. T. Craig, Introduction to Mathematical Statistics, Fourth. 1970.
  17. Algifari, Analisis Regresi, Teori, Kasus dan Solusi. Yogyakarta: BPFE UGM, 2000.
  18. S. Andriani, Uji Park Dan Uji Breusch Pagan Godfrey Dalam Pendeteksian Heteroskedastisitas Pada Analisis Regresi, Al-Jabar J. Pendidik. Mat., 8(1) (2017) 63–72.
  19. J. Durbin and G. S. Watson, Testing for Serial Correlation in Least Squares Regression II, Biometrika, 38 (1951) 159–177.
  20. M. Sriningsih, D. Hatidja, and J. D. Prang, Penanganan Multikolinearitas Dengan Menggunakan Analisis Regresi Komponen Utama Pada Kasus Impor Beras Di Provinsi Sulut, J. Ilm. Sains, 18(1) 92018) 18.
  21. A. M. Seheult, A. H., Green, P. J., Rousseeuw, P. J., & Leroy, Robust Regression and Outlier Detection. John wiley & sons., 2005.
  22. G. E. P. Box, Non-Normality and Tests on Variances, Biometrika, 40, (1953).
  23. P. J. Huber, Robust Statistics. Berlin Heidelberg: Springer, 2011.
  24. J. W. Tukey, Conclusions vs Decisions, Technometrics, 2 (2012) 423–433.
  25. D. H. Huber Jr, E. E., and Ridgley, Magnetic Properties of a Single Crystal of Manganese Phosphide, Phys. Rev., 1964.
  26. F. R. Hampel, Contributions to the Theory of Robust Estimation., 1968.
  27. C. Chen, Robust Regression and Outlier Detection with the ROBUSTREG Procedure, SAS Inst. Inc., 9 (2002) 25–27.
  28. Y. dan Susanti, Estimasi-M dan Sifat-sifatnya pada Regresi Linear Robust., Math-Info, 2008.
  29. P. R. & V. Yohai, Robust Regression by Means of S-Estimators. New York: Springer, 1984.
  30. M. S.-B. RA Maronna, RD Martin, VJ Yohai, Robust Statistics: Theory and Methods (with R). 2019.