Robust Geographically and Temporally Weighted Regression Using S-estimator in Criminal Case in East Java Province

  • Zikalta Putra Department of Statistics, IPB University, Bogor, 16680, Indonesia
  • Hari Wijayanto Department of Statistics, IPB University, Bogor, 16680, Indonesia
  • Muhammad Nur Aidi Department of Statistics, IPB University, Bogor, 16680, Indonesia
Keywords: GWR, GTWR, S-estimator, RMSE, MAD, crime rate


Geographically weighted regression (GWR) is a model that can be used for data with spatial varying. Geographically and Temporally Weighted Regression (GTWR) is a development of the GWR model for data spatial and temporal varying. Parameter estimation in GTWR model uses weighted least square method which is very sensitive to outliers data. The outlier caused bias in parameter estimation, so it must be handled by robust GTWR (RGTWR). In this research, S-estimator was used to handle outliers and estimate an RGTWR. Both GTWR and RGTWR is used to build model crime rate in East Java 2011-2015.  The Crime rate is used as a response variable and the percentage of poor people, population density, and human development index are used as explanatory variables. The best model in this research is RGTWR using S-estimator. RGTWR using S-estimator has a coefficient of determination equal to 98,2  meanwhile RMSE equal to 33.941 and MAD equal to 4.994.


[BPS] Badan Pusat Statistik Jawa Timur. Provinsi Jawa Timur dalam Angka 2011-2015. Jawa Timur (ID): BPS. 2011-2015.

[BPS] Badan Pusat Statistik. Statistik Kriminal 2017. Jakarta (ID): BPS. 2017.

Dona FM, Setiawan. "Pemodelan Faktor-Faktor Yang Mempengaruhi Tingkat Kriminalitas di Jawa Timur dengan Analisis Regresi Spasial". Jurnal Sains dan Seni ITS, vol. 4, no 1. 2015.

Erda G, Indahwati, A Djuraidah. "Outlier handling of robust geographically and temporally weighted regression". Journal of Physics: Conference Series, vol. 1175. 2019.

Farber S., Pa´ez A. "A Systematic Investigation of Cross-Validation in GWR Model Estimation: Empirical Analysis and Monte Carlo Simulations". Journal of Geographical Systems, vol. 9, pp. 371–396. 2007.

Fotheringham AS, Brundson C, Charlton M. “Geographically Weighted Regression: The Analysis of Spatially Varying Relationship”. England: John Wiley & Sons Ltd., 2002, pp. 1-22.

Fotheringham AS, Crespo R, Yao J. “Geographically and temporal weighted regression (GTWR)”. Geographical Analysis. The Ohio State University: 1-22. 2015.

Huang B, Wu B, Barry M. "Geographically and Temporally Weighted Regression for Modeling Spatio-Temporal Variation in House Prices". International Journal Of Geographical Information Science, vol. 24 (3), pp. 383-401. 2010.

Liu H., Jezek K, and O’Kelly M.. "Detecting Outliers In Irregularly Distributed Spatial Datasets by Locally Adaptive and Robust Statistical Analysis and GIS". International Journal of Geographical Information Science, vol. 15, pp. 721–741. 2001.

Liu J, Yang Y, Xu S, Zhao Y, Wang Y, Zhang F. “A Geographically Temporal Weighted Regression Approach With Travel Distance for House Price Estimation”. Article Entropy MDPI, vol. 303 (18), pp. 1-13. 2017.

Rousseeuw PJ, Yohai VJ. “Robust Regression by Means of S-Estimators, Robust and Nonlinear Time Series Analysis”. Lecture Notes in Statistics 26, pp. 256–272. 1984.

Sholihin M, Agus MS, A Djuraidah. "Geographically and Temporally Weighted Regression (GTWR) for Modeling Economic Growth Using R". International Journal of Computer Science and Network, vol. 6, pp. 2277-5420. 2017.

Simamora PA, Vita R. "Pemodelan Persentase dan Faktor-Faktor Yang Mempengaruhi di Jawa Timur dengan Pendekatan GWR". Jurnal Sains dan Seni ITS, vol. 3, no. 1. 2014.

Wang P. "Exploring Spatial Effects on Housing Price: The Case Study of The City of Calgary". Master dissertation. University of Calgary, Canada. 2006.

Widiyanti KY, Yasin H, Sugito. "Pemodelan Proporsi Penduduk Miskin Kabupaten dan Kota di Provinsi Jawa Tengah Menggunakan Geographically and Temporally Weighted Regression". Jurnal Gaussian, vol. 3(4), pp. 691-700. 2014.

Y Susanti and H Pratiwi. “M estimation, S estimation, and MM estimation in Robust Regression”. International Journal of Pure and Applied Mathematics, vol .91, no 9, pp 349-360. 2014.