Quantile Regression, Robust LTS, Parameter Estimation, Outlier, Dengue, Lampung

Anggun Setia Pramesthi; Dorrah Azis; Tiryono Ruby; Khoirin Nisa

doi:10.59890/ijasse.v3i4.124

Authors

Anggun Setia Pramesthi University of Lampung
Dorrah Azis University of Lampung
Tiryono Ruby University of Lampung
Khoirin Nisa University of Lampung

DOI:

https://doi.org/10.59890/ijasse.v3i4.124

Keywords:

Quantile Regression, Robust LTS, Parameter Estimation, Outlier, Dengue, Lampung

Abstract

This study compares the Quantile regression method with the robust Least Trimmed squares (LTS) regression in analyzing the factors influencing the incidence of Dengue Hemorrhagic Fever (DHF) in Lampung Province. The data used consist of five independent variables: population density, environmental sanitation, rainfall, health center ratio, and doctor ratio. Parameter estimation was carried out at several quantiles, namely τ = 0.05, 0.25, 0.50, 0.75, and 0.95, and was compared with the results of the OLS and LTS models. The results show that the quantile regression model at the τ = 0, 95 quantile is the best model with a coefficient of determination (R2 ) of 0.8088. This model is better able to capture the influence of variables on extreme DHF cases and is more robust to outliers compared to the OLS model (R2 = 0.225) and the LTS model (R2 = −0.1453). The factors that have a significant effect on the best model include environmental sanitation, rainfall, population density, and the health center ratio.

References

Azhari, M., Iskandar, I., & Putri, D. (2023). Genetic variations and their implications in dengue virus infection: A study in Indonesia. BMC Infectious Diseases, 23(1), 456.

Badan Pusat Statistik Provinsi Lampung. (2024). Statistik Kesehatan Pro- vinsi Lampung 2018–2023: Penyakit Demam Berdarah Dengue. Bandar Lampung: BPS Provinsi Lampung. Diakses pada 5 Januari 2025, dari ht- tps://lampung.bps.go.id

Badan Pusat Statistik Provinsi Lampung. (2024). Penyakit Demam Berdarah Dengue 2024. Bandar Lampung: BPS Provinsi Lampung. Diakses pada 5 April 2025, dari https://lampung.bps.go.id

Bai, Y., Zhang, L., & Wang, Y. (2021). Clinical features and risk factors of severe dengue fever: A systematic review and meta-analysis. PLOS Neglected Tropical Diseases.

Basuki, S. (2016). Gejala dan penanganan demam berdarah dengue di Indo- nesia. Jurnal Kesehatan Masyarakat Nasional, 10(2), 123–130.

Chen, C., & Wei, Y. (2005). Computational issues for quantile regression. Sankhya¯: The Indian Journal of Statistics, 67(2), 399–417.

Davino, C., Furno, M., & Vistocco, D. (2014). Quantile Regression: Theory and Applications. Stanford Weisberg.

Dinas Kesehatan Provinsi Lampung. (2022). Laporan Tahunan Kasus DBD Provinsi Lampung Tahun 2022. Bandar Lampung: Dinas Ke- sehatan Provinsi Lampung. Diakses pada 3 Januari 2025, dari ht- tps://dinkes.lampungprov.go.id

Effendi, R., Maiyastri, M., & Diana, R. (2019). Perbandingan metode re- gresi kuantil dan metode Bayes dalam mengestimasi parameter model re- gresi linier sederhana dengan galat heteroskedastisitas. Jurnal Matematika UNAND, 8(2), 291–298.

Faiz, S. A., & Hartono, B. (2023). Faktor risiko demam berdarah dengue di Indonesia: Studi kasus di 10 provinsi. Jurnal Manajemen Kesehatan Yayasan RS Dr. Soetomo, 9(1), 45–56.

Frost, J. (2020, Mei 15). How to interpret R-squared in regression analysis. Statistics By Jim.

Ghozali, Imam. (2013). Aplikasi Analisis Multivariat dengan Program IBM SPSS (Edisi 7). Semarang: Badan Penerbit Universitas Diponegoro.

Gob, S. C. & Knight, K. (2009). Nonstandard quantile-regression inference. Econometric Theory, 25(5), 1415–1432.

Houghton, R., Dyer, J., & Smith, J. (2021). Asymptomatic dengue infection in Southeast Asia: A systematic review. Tropical Medicine and Infectious Disease, 6(3), 156.

Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679–688.

Kementerian Kesehatan Republik Indonesia. (2015). Pedoman Nasional Pelayanan Kedokteran Tatalaksana Demam Berdarah Dengue. Jakar- ta: Kementerian Kesehatan RI. Diakses pada 6 Januari 2025, dari ht- tps://pusdatin.kemkes.go.id

Kementerian Kesehatan Republik Indonesia. (2020). Profil Kesehatan Indo- nesia Tahun 2020. Jakarta: Kementerian Kesehatan RI. Diakses pada 6 Ja- nuari 2025, dari https://pusdatin.kemkes.go.id

Koenker, R. (2020). Quantile Regression (Edisi ke-2). Cambridge: Cambridge University Press.

Myers, R. H. (1990). Classical and Modern Regression with Applications (Edisi ke-2). Boston: PWS-Kent.

Rachmawati, R., Santoso, B., & Utami, S. (2021). The impact of climate change on dengue fever incidence in urban areas of Indonesia. Environmental Research, 194, 110678.

SAS Institute Inc. (2017). Five things you should know about quantile regression [Paper 1482-2017]. SAS Global Forum 2017 Proceedings.

Septian, A., Anwar, M. C., & Marsum, M. (2017). Studi korelasi bebera- pa faktor yang mempengaruhi kejadian demam berdarah dengue di Kabu- paten Banyumas tahun 2010–2015. Buletin Penelitian Kesehatan, 45(3), 230–238.

Setyowati, E., Akbarita, R., & Robby, R. R. (2021). Perbandingan regresi ro- bust metode least trimmed square (LTS) dan metode estimasi-S pada pro- duksi padi. Jurnal Matematika UNAND, 10(3), 329–341.

Supriyadi, A., Rahman, A., & Farhan, M. (2022). Environmental factors influencing Aedes aegypti breeding sites in urban Indonesia. Journal of En- Environmental Health Science & Engineering, 20(1), 123–132.

Triwahyuni, T., Husna, I., & Andesti, M. (2020). Hubungan curah hujan de- ngan kasus demam berdarah dengue di Bandar Lampung 2016–2018. Jur- nal Ilmu Kesehatan Masyarakat, 11(3), 184–199.

Walpole, R. E. (1993). Pengantar Statistika (Edisi ke-3, Terjemahan oleh Su- mantri, B.). Jakarta: Gramedia Pustaka Utama.

World Health Organization. (2021, Maret 17). Dengue and severe dengue. Geneva: World Health Organization. Diakses pada 10 Januari 2025, dari https://www.who.int/news-room/fact-sheets/detail/dengue-and- severe-dengue