Modeling the Number of Maternal Deaths in East Java Province Using  MM-Estimation and GM-Estimation Robust Regression

Wijanarko Rifqi   Nugroho; Yuliana   Susanti; Isnandar   Slamet

Wijanarko Rifqi Nugroho Study Program of Statistics Sebelas Maret University, Indonesia, 57126
Yuliana Susanti Study Program of Statistics Sebelas Maret University, Indonesia, 57126
Isnandar Slamet Study Program of Statistics Sebelas Maret University, Indonesia, 57126

Abstrak

Maternal Mortality Rate (MMR) is one of the targets of the Sustainable Development Goals (SDGs), and MMR is set to be less than 70 per 100,000 live births by 2030. The MMR in Indonesia in 1991-2020 decreased from 390 to 189 per 100,000 live births. The reduction in MMR is still far from the target set by the SDGs. In 2022, the number of maternal deaths in Indonesia was 3,572, with East Java Province as a large contributor of 486 deaths. The aims of the research are the number of maternal deaths ( , the number of mothers experiencing hypertension ( , the number of mothers experiencing bleeding ( , the number of mothers experiencing infections ( , and the number of specialized hospitals ( . The methods used in this research are MM-Estimation and GM-Estimation robust regression. Robust regression was used because the data has outliers, so the residuals are not normally distributed. The results showed that the MM-Estimation and GM-Estimation model has an Adjusted R-squared value of 85.98% and 91.88% and AIC value of 201.1614 and 183.4612, with all independent variables significantly affecting maternal mortality. Based on the analysis, it is concluded that the robust regression GM-Estimation model is better than the MM-Estimation model because it has a larger Adjusted R-squared value and a smaller AIC value. The robust regression GM-Estimation model has the following equation: =1.893021+1.331650 +1.653501 +2.099621 -1.139574 .

Referensi

Andriany, C. D., Susanti, Y., & Sugiyanto. (2021). Estimasi Parameter Regresi Robust dengan Metode Estimasi Least Trimmed Squares (LTS) Pada Kematian Ibu Di Indonesia. Prosiding Seminar Nasional Aplikasi Sains & Teknologi (SNAST), 9–14.
Ayinde, K., Lukman, A. F., & Arowolo, O. (2015). Robust Regression Diagnostics of Influential Observations in Linear Regression Model. Open Journal of Statistics, 05(04), 273–283. https://doi.org/10.4236/ojs.2015.54029
Febriyanto, E. C., Indawati, R., Mahmudah, Ama, F., & Ashari, F. Y. (2023). Modeling of Maternal Mortality (Mmr) in East Java 2017-2019 Using Panel Regression Approach. Jurnal Biometrika Dan Kependudukan, 12(2), 177–185. https://doi.org/10.20473/jbk.v12i2.2023.177-185
Huber, P. J. (1964). Robust Estimation of a Location Parameter. The Annals of Mathematical Statistics, 35(1), 73–101. https://doi.org/10.1214/aoms/1177703732
Kamel, A., & Abonazel, M. R. (2023). A Simple Introduction to Regression Modeling using R. Computational Journal of Mathematical and Statistical Sciences, 2(1), 52–79. https://doi.org/10.21608/cjmss.2023.189834.1002
Kementerian Kesehatan RI. (2023). Profil Kesehatan Indonesia 2022. Kementerian Kesehatan Republik Indonesia. https://kemkes.go.id/id/profil-kesehatan-indonesia-2022
Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to Linear Regression Analysis Sixth Edition. In Munro’s Statistical Methods for Health Care Research: Sixth Edition. https://doi.org/10.4324/9780203499894-15
Pek, J., Wong, O., & Wong, A. C. M. (2018). How to address non-normality: A taxonomy of approaches, reviewed, and illustrated. Frontiers in Psychology, 9, 1–17. https://doi.org/10.3389/fpsyg.2018.02104
Prahutama, A., & Rusgiyono, A. (2021). Robust regression with MM-estimator for modelling the number maternal mortality of pregnancy in Central Java, Indonesia. Journal of Physics: Conference Series, 1943(1), 1–7. https://doi.org/10.1088/1742-6596/1943/1/012148
Rasheed, B. A., Adnan, R., Saffari, S. E., & Pati, K. D. (2014). Robust weighted least squares estimation of regression parameter in the presence of outliers and heteroscedastic errors. Jurnal Teknologi, 71(1), 11–18. https://doi.org/10.11113/jt.v71.3609
Rousseeuw, P., & Yohai, V. (1984). Robust Regression By Means of S-estimators. In Robust and nonlinear time series analysis : Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 “Stochastische Mathematische Modelle”, Heidelberg 1983 (pp. 256–272). https://doi.org/10.1007/978-1-4615-7821-5-15
Sabzekar, M., & Hasheminejad, S. M. H. (2021). Robust regression using support vector regressions. Chaos, Solitons and Fractals, 144, 110738. https://doi.org/10.1016/j.chaos.2021.110738
Say, L., Chou, D., Gemmill, A., Tunçalp, Ö., Moller, A. B., Daniels, J., Gülmezoglu, A. M., Temmerman, M., & Alkema, L. (2014). Global causes of maternal death: A WHO systematic analysis. The Lancet Global Health, 2(6), 323–333. https://doi.org/10.1016/S2214-109X(14)70227-X
Susanti, Y., Pratiwi, H., Sulistijowati, S., & Liana, T. (2014). M Estimation, S Estimation, and MM Estimation in Robust Regression. International Journal of Pure and Applied Mathematics, 91(3), 349–360. https://doi.org/10.12732/ijpam.v91i3.7
United Nations. (2016). Transforming Our World : The 2030 Agenda for Sustainable Development. Arsenic Research and Global Sustainability - Proceedings of the 6th International Congress on Arsenic in the Environment, AS 2016. https://doi.org/10.1201/b20466-7
Wilcox, R. (2012). Introduction to Robust Estimation and Hypothesis Testing. In Academic Press. https://doi.org/10.1016/b978-0-12-386983-8.00010-x
Yu, C., & Yao, W. (2017). Robust linear regression: A review and comparison. Communications in Statistics - Simulation and Computation, 46(8), 6261–6282. https://doi.org/10.1080/03610918.2016.1202271