GEOGRAPHICALLY WEIGHTED GENERALIZED POISSON REGRESSION AND GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL REGRESSION MODELING ON PROPERTY CRIME CASES IN CENTRAL JAVA

  • Prizka Rismawati Arum Departement of Statistic, Faculty of Science and Agricultural Technology, Universitas Muhammadiyah Semarang, Indonesia https://orcid.org/0000-0003-1577-0596
  • Rahmad Putra Gautama Departement of Statistic, Faculty of Science and Agricultural Technology, Universitas Muhammadiyah Semarang, Indonesia https://orcid.org/0009-0009-1476-4929
  • M. Al Haris Departement of Statistic, Faculty of Science and Agricultural Technology, Universitas Muhammadiyah Semarang, Indonesia https://orcid.org/0000-0003-3702-3161
DOI: https://doi.org/10.30598/barekengvol19iss3pp1469-1484
Keywords: Adaptive Bisquare Kernel, Geographically Weighted Generalized Poisson Regression, Geographically Weighted Negative Binomial Regression, Overdispersion, Property Crime

Abstract

Property crime in Indonesia remains one of the most prevalent categories of crime across various regions of the country. This category encompasses a range of criminal acts, including theft, illegal appropriation of goods, robbery, motor vehicle theft, arson, and property damage. One of the commonly used regression analysis methods is Poisson regression. The assumption violation of overdispersion in Poisson regression is often found in property crime data in Central Java. This study also considers spatial aspects, depicting local regional characteristics and the integration of local and global variables. Therefore, this study employs Geographically Weighted Generalized Poisson Regression (GWGPR) and Geographically Weighted Negative Binomial Regression (GWNBR) methods with Adaptive Bisquare Kernel weighting. The aim of this research is to develop a model for each district/city in Central Java using Adaptive Bisquare Kernel weighting, thus providing a more accurate representation of the factors influencing property crime in each region. The AIC value criterion of 411.3652 indicates that the GWNBR method is the most suitable for modeling the number of property crime cases in each district/city in Central Java compared to Poisson regression, negative binomial regression, and GWGPR methods.

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References

Y. Yigzaw, A. Mekuriaw, dan T. Amsalu, “ANALYZING PHYSICAL AND SOCIO-ECONOMIC FACTORS FOR PROPERTY CRIME INCIDENT IN ADDIS ABABA, ETHIOPIA,” Heliyon, vol. 9, no. 2, hal. e13282, 2023, doi: https://doi.org/10.1016/j.heliyon.2023.e13282.

B. J. Ficarra, INCARCERATED CONGENITAL DIAPHRAGMATIC HERNIA, vol. 92, no. 3. 1956. doi: https://doi.org/10.1016/S0002-9610(56)80126-8.

Lance Lochner, "Education, Work and Crime: Theory and Evidence," New York, University of Rochester, 1999, pp. 2-3.

S. M. T. Situmaeng, BUKU AJAR KRIMINOLOGI. 2021.

B. A. Wisudaningsi, I. Arofah, dan K. A. Belang, “PENGARUH KUALITAS PELAYANAN DAN KUALITAS PRODUK TERHADAP KEPUASAN KONSUMEN DENGAN MENGGUNAKAN METODE ANALISIS REGRESI LINEAR BERGANDA,” Statmat J. Stat. Dan Mat., vol. 1, no. 1, hal. 103–117, 2019, doi: https://doi.org/10.32493/sm.v1i1.2377.

S. W. Tyas, Gunardi, dan L. A. Puspitasari, “GEOGRAPHICALLY WEIGHTED GENERALIZED POISSON REGRESSION MODEL WITH THE BEST KERNEL FUNCTION IN THE CASE OF THE NUMBER OF POSTPARTUM MATERNAL MORTALITY IN EAST JAVA,” MethodsX, vol. 10, no. October 2022, hal. 102002, 2023, doi: https://doi.org/10.1016/j.mex.2023.102002.

N. M. R. Keswari, I. W. Sumarjaya, dan N. L. P. Suciptawati, “PERBANDINGAN REGRESI BINOMIAL NEGATIF DAN REGRESI GENERALISASI POISSON DALAM MENGATASI OVERDISPERSI (STUDI KASUS: JUMLAH TENAGA KERJA USAHA PENCETAK GENTENG DI BR. DUKUH, DESA PEJATEN),” E-Jurnal Mat., vol. 3, no. 3, hal. 107, 2014, doi: https://doi.org/10.24843/mtk.2014.v03.i03.p072.

D. Rahmadini, I. N. Manfaati, dan P. A. Rismawati, “PEMODELAN BIVARIATE GENERALIZED POISSON REGRESSION PADA KASUS ANGKA KEMATIAN DI PROVINSI JAWA TENGAH,” Pros. Semin. Nas. UNIMUS, vol. 6, hal. 401–410, 2023, [Daring]. Tersedia pada: https://prosiding.unimus.ac.id/index.php/semnas/article/view/1482

W. Pratama dan S. P. Wulandari, “PEMETAAN DAN PEMODELAN JUMLAH KASUS PENYAKIT TUBERCULOSIS (TBC) DI PROVINSI JAWA BARAT DENGAN PENDEKATAN GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL REGRESSION,” J. Sains dan Seni ITS, vol. 4, no. 1, hal. 37–42, 2015.

M. Adryanta dan P. Purhadi, “ANALISIS METODE GEOGRAPHICALLY WEIGHTED GENERALIZED POISSON REGRESSION UNTUK PEMODELAN FAKTOR YANG MEMPENGARUHI JUMLAH KEMATIAN ANAK DI PROVINSI JAWA TIMUR,” J. Sains dan Seni ITS, vol. 8, no. 2, 2020, doi: https://doi.org/10.12962/j23373520.v8i2.43562.

Desriwendi, Abdul Hoyyi, dan Triastuti Wuryandari, “PEMODELAN GEOGRAPHICALLY WEIGHTED LOGISTIC REGRESSION (GWLR) DENGAN FUNGSI PEMBOBOT FIXED GAUSSIAN KERNEL DAN ADAPTIVE GAUSSIAN KERNEL (STUDI KASUS : LAJU PERTUMBUHAN PENDUDUK PROVINSI JAWA TENGAH),” J. Gaussian, vol. 4, no. 2, hal. 193–204, 2015.

D. L. Sogen, P. R. Arum, dan R. Wasono, “PEMODELAN GEOGRAPHICALLY WEIGHTED POISSON REGRESSION (GWPR) DENGAN PEMBOBOT FIXED BISQUARE KERNEL DAN ADAPTIVE BISQUARE KERNEL PADA KASUS DBD DI RIAU GEOGRAPHICALLY WEIGHTED POISSON REGRESSION (GWPR) MODELING WITH FIXED BISQUARE KERNEL AND ADAPTIVE BISQUA,” Semin. Nas. Publ. Hasil-Hasil Penelit. dan Pengabdi. Masy., vol. 6, no. 18 Oktober 2023, hal. 371–387, 2023.

E. Supriyadi, S. Mariani, dan Sugiman, “PERBANDINGAN METODE PARTIAL LEAST SQUARE ( PLS ) DAN,” Unnes J. Math., vol. 6, no. 2, hal. 117–128, 2017.

P. R. Arum dan S. Alfian, “PEMODELAN PERTUMBUHAN EKONOMI DI JAWA BARAT MENGGUNAKAN METODE GEOGRAPHICALLY WEIGHTED PANEL REGRESSION,” J Stat. J. Ilm. Teor. dan Apl. Stat., vol. 15, no. 2, hal. 219–227, 2022, doi: https://doi.org/10.36456/jstat.vol15.no2.a5506.

K. A. Yulianingsih, K. G. Gde, dan L. P. Suciptawati, “PENERAPAN REGRESI POISSON UNTUK MENGETAHUI FAKTOR-FAKTOR YANG MEMENGARUHI JUMLAH SISWA SMA/SMK YANG TIDAK LULUS UN DI BALI,” e-Jurnal Mat., vol. 1, no. Agustus, hal. 59–63, 2012.

W. Sabtika, A. Prahutama, dan H. Yasin, “PEMODELAN GEOGRAPHICALLY WEIGHTED GENERALIZED POISSON REGRESSION (GWGPR) PADA KASUS KEMATIAN IBU NIFAS DI JAWA TENGAH,” J. Gaussian, vol. 10, no. 2, hal. 259–268, 2021, doi: https://doi.org/10.14710/j.gauss.v10i2.30946.

A. Rahayu, “MODEL-MODEL REGRESI UNTUK MENGATASI MASALAH OVERDIPERSI PADA REGRESI POISSON,” J. Peqguruang Conf. Ser., vol. 2, no. 1, hal. 1, 2021, doi: https://doi.org/10.35329/jp.v2i1.1866.

K. Antonio dan J. Beirlant, “ACTUARIAL STATISTICS WITH GENERALIZED LINEAR MIXED MODELS,” Insur. Math. Econ., vol. 40, no. 1, hal. 58–76, 2007, doi: https://doi.org/10.1016/j.insmatheco.2006.02.013.

M. Beisemann, “A FLEXIBLE APPROACH TO MODELLING OVER-, UNDER- AND EQUIDISPERSED COUNT DATA IN IRT: THE TWO-PARAMETER CONWAY–MAXWELL–POISSON MODEL,” Br. J. Math. Stat. Psychol., vol. 75, no. 3, hal. 411–443, 2022, doi: https://doi.org/10.1111/bmsp.12273.

A. G. Halunga, C. D. Orme, dan T. Yamagata, A HETEROSKEDASTICITY ROBUST BREUSCH–PAGAN TEST FOR CONTEMPORANEOUS CORRELATION IN DYNAMIC PANEL DATA MODELS, vol. 198, no. 2. 2017. doi: https://doi.org/10.1016/j.jeconom.2016.12.005.

P. Rismawati Arum, R. Putra Gautama, I. Fitriani, dan F. Naza Nurvahyani, “IDENTIFYING FACTORS THAT INFLUENCE LIFE EXPECTANCY IN CENTRAL JAVA USING SPATIAL REGRESSION MODELS,” J Stat., vol. 16, no. 2, hal. 605–613, 2023.

M. Al Haris dan P. R. Arum, “NEGATIVE BINOMIAL REGRESSION AND GENERALIZED POISSON REGRESSION MODELS ON THE NUMBER OF TRAFFIC ACCIDENTS IN CENTRAL JAVA,” BAREKENG J. Ilmu Mat. dan Terap., vol. 16, no. 2, hal. 471–482, 2022, doi: https://doi.org/10.30598/barekengvol16iss2pp471-482.

C. Raschke dan W. H. Greene, “ERRATUM TO FUNCTIONAL FORMS FOR THE NEGATIVE BINOMIAL MODEL FOR COUNT DATA [ECONOMICS LETTERS 99, (2008), 585-590],” Econ. Lett., vol. 107, no. 2, hal. 313, 2010, doi: https://doi.org/10.1016/j.econlet.2009.09.026.

Y. Wibawati, “MAXIMUM LIKELIHOOD ESTIMATION MODEL LINEAR DAN LOG-LINEAR DALAM REGRESI POISSON,” no. 3, hal. 181–188, 2009.

E. U. L. Fitri, “PEMODELAN FAKTOR-FAKTOR YANG MEMPENGARUHI JUMLAH KASUS TUBERKULOSIS DI JAWA TIMUR MENGGUNAKAN METODE GEOGRAPHICALLY WEIGHTED GENERALIZED POISSON REGRESSION DAN GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL REGRESSION,” 2017.

B. W. Y. Priambodo dan I. Irhamah, “PEMETAAN JUMLAH PROPERTY CRIME DI PROVINSI JAWA TIMUR MENGGUNAKAN METODE GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL REGRESSION (GWNBR) DAN GEOGRAPHICALLY WEIGHTED POISSON REGRESSION (GWPR),” Inferensi, vol. 2, no. 2, hal. 53, 2019, doi: https://doi.org/10.12962/j27213862.v2i2.6818.

T. Nakaya, A. S. Fotheringham, C. Brunsdon, dan M. Charlton, “GEOGRAPHICALLY WEIGHTED POISSON REGRESSION FOR DISEASE ASSOCIATION MAPPING,” Stat. Med., vol. 24, no. 17, hal. 2695–2717, 2005, doi: https://doi.org/10.1002/sim.2129.

R. P. Gautama, “PENGARUH PENGELUARAN PERKAPITA, JUMLAH PENDUDUK MISKIN, TINGKAT PENGANGGURAN TERBUKA (TPT), DAN TINGKAT PARTISIPASI ANGKATAN KERJA (TPAK) TERHADAP PENDAPATAN PAJAK PROVINSI JAWA TENGAH,” Emerg. Stat. Data Sci. J., vol. 2, no. 1, hal. 97–106, 2024, doi: https://doi.org/10.20885/esds.vol2.iss.1.art10.

Published
2025-07-01
How to Cite
[1]
P. R. Arum, R. P. Gautama, and M. A. Haris, “GEOGRAPHICALLY WEIGHTED GENERALIZED POISSON REGRESSION AND GEOGRAPHICALLY WEIGHTED NEGATIVE BINOMIAL REGRESSION MODELING ON PROPERTY CRIME CASES IN CENTRAL JAVA”, BAREKENG: J. Math. & App., vol. 19, no. 3, pp. 1469-1484, Jul. 2025.
Issue
Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
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Articles

Copyright (c) 2025 Prizka Rismawati Arum, Rahmad Putra Gautama, M. Al Haris

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