Mali, Elisabeth Vianey (2026) Model Geographically Weighted Bivariate Generalized Weibull Regression (Studi Kasus: Angka Harapan Hidup dan Kemiskinan di Provinsi Jawa Tengah dan Daerah Istimewa Yogyakarta Tahun 2023). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Bivariate Generalized Weibull Regression (BGWR) merupakan regresi dengan dua variabel respon yang berkorelasi danberdistribusi Generalized Weibull. Pemodelan ini menghasilkan taksiran parameter yang bersifat global untuk seluruh lokasi pengamatan. Unit penelitian berupa lokasi memungkinkan terjadinya efek spasial, untuk itu diperlukan analisis yang dapat mencakup pengaruh lokasi tersebut dengan pemodelan Geographically Weighted Bivariate Generalized Weibull Regression (GWBGWR). GWBGWR merupakan pengembangan dari BGWR dengan menambahkan efek spasial berupa koordintaslintang dan bujur sehingga menghasilkan penaksir parameter yang bersifat lokal untuk setiap lokasi pengamatan. Pada penelitian ini dibahas mengenai estimasi parameter dan statistik uji untuk model BGWR dan GWBGWR. Hasil penelitian ini menunjukkan bahwa penaksiran parameter model BGWR dan GWBGWR menggunakan Maximum Likelihood Estimation (MLE) menghasilkan persamaan yang tidak closed-form sehingga diselesaikan dengan iterasi numerik Berndt-Hall-Hall-Hausman (BHHH). Statistik uji untuk pengujian serentak menggunakan metode Maximum Likelihood Ratio Test (MLRT). Selanjutnya model diaplikasikan pada Angka Harapan Hidup dan Persentase Penduduk Miskin di Provinsi Jawa Tengah dan Daerah Istimewa Yogyakarta tahun 2023. Pemodelan menggunakan GWBGWR menghasilkan 6 kelompok kabupaten/kota berdasarkan variabel yang signifikan terhadap Angka Harapan Hidup dan 3 kelompok kabupaten/kota berdasarkan variabel Persentase Penduduk Miskin. Variabel Rata-rata Lama Sekolah berpengaruh signifikan terhadap Angka Harapan Hidup dan Persentase Penduduk Miskin di semua kabupaten/kota.Sementara itu, Laju Pertumbuhan Ekonomi, Tingkat Pengangguran Terbuka, Rasio Tenaga Kesehatan, Tingkat Partisipasi Angkatan Kerja, dan Angka Partisipasi Kasar SMA memiliki signifikansi yang bervariasi antar lokasi. Kebaikan model diukur dengan AICc. Nilai AICc model GWBGWR menggunakan kernel Fixed Bisquare lebih kecil dibandingkan dengan model BGWR dan model GWBGWR menggunakan kernel lainnya, sehingga disimpulkan bahwa GWBGWR menggunakan kernel Fixed Bisquare lebih baik untuk memodelkan Angka Harapan Hidup dan Persentase Penduduk Miskin di Provinsi Jawa Tengah dan Daerah Istimewa Yogyakarta tahun 2023.
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Bivariate Generalized Weibull Regression (BGWR) is a regression with two correlated response variables distributed according to the Generalized Weibull distribution. This model produces global parameter estimates for all observation locations. Research units in the form of locations allows for spatial effects, therefore an analysis that can cover the influence of the locations is required using Geographycally Weighthed Bivariate Generalized Weibull Regression (GWBGWR) modelling. GWBGWR is an extension of BGWR with the addition of spatial effects in the form of latitude and longitude coordinates, resulting in local parameter estimation for each observation location. This study discusses parameter estimation and test statistics for the BGWR and GWBGWR models using Maximum Likelihood Estimation (MLE) produces equations that are not closed-form, so they are solved using Berndt-Hall-Hall-Hausman (BHHH) numerical iteration. Test statistics for simultaneous testing use the Maximum Likelihood Ratio Test (MLRT) method. Furthermore, the model is applied to Life Expectancy and the Percentage of Poor People in Central Java Province and The Special Region of Yogyakarta in 2023. Modeling using GWBGWR produced 6 groups of districts/cities based on variables that were significant to Life Expectancy and 3 groups of districts/cities based on the Poverty Rate variable. The average Length of Schooling variable had a significant effect on Life Expectancy and the Percentage of Poor People in all districts/cities. Meanwhile, the Economic Growth Rate, Open Unemployment Rate, Health Worker Ratio, Labor Force Participation Rate, and Gross High School Enrollment Rate had varying significance between locations. Model goodness is measured by AICc. The AICc value of the GWBGWR model using the Fixed Bisquare kernel is smaller than that of the BGWR model and the GWBGWR model using other kernels, so it can be concluded that GWBGWR using the Fixed Bisquare kernel is better for modeling life expectancy and the percentage of poor people in Central Java Province and the Special Region of Yogyakarta in
2023.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Distribusi Bivariate Generalized Weibull, Bivariate Generalized Weibull Regression, Geographically Weighted Bivariate Generalized Weibull Regression, Angka Harapan Hidup dan Kemiskinan. Bivariate Generalized Weibull Distribution, Bivariate Generalized Weibull Regression, Geographically Weighted Bivariate Generalized Weibull Regression, Life Expectancy and Poverty. |
| Subjects: | Q Science > QA Mathematics > QA276 Mathematical statistics. Time-series analysis. Failure time data analysis. Survival analysis (Biometry) |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Elisabeth Vianey Mali |
| Date Deposited: | 14 Jan 2026 05:44 |
| Last Modified: | 14 Jan 2026 05:44 |
| URI: | http://repository.its.ac.id/id/eprint/129602 |
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