Ningrum, Christin (2022) Penaksiran Parameter Dan Pengujian Hipotesis Geographically And Temporally Weighted Bivariate Binomial Negative Regression (Studi Kasus : Jumlah Kematian Ibu Dan Jumlah Kematian Bayi Di Provinsi Jawa Tengah 2016-2020). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Negative Binomial Regression (NBR) merupakan salah satu alternatif pemodelan ketika respon diskret dan terjadi pelanggaran asumsi ekuidispersi. Ketika terdapat dua respon count yang saling berkorelasi dan terjadi pelanggaran asumsi ekuidispersi, maka salah satu model yang tepat untuk digunakan adalah Bivariate Negative Binomial Regression (BNBR). Pemodelan BNBR dilakukan dengan dan tanpa variabel exposure. Model BNBR dengan variabel exposure memiliki akurasi terbaik dengan RMSE terkecil dan R2 yang lebih besar. Penelitian ini mengkaji metode BNBR exposure yang mengakomodir heterogenitas spasial dan temporal karena data yang digunakan berupa panel dengan unit observasi berupa wilayah yang dikenal dengan Geographically and Temporally Weighted Bivariate Negative Binomial Regression (GTWBNBR) dengan variabel expsoure. Pemodelan diterapkan pada kasus jumlah kematian ibu dan jumlah kematian bayi di Provinsi Jawa Tengah tahun 2016-2020. Estimasi parameter model GTWBNBR exposure menggunakan Maximum Likelihood Estimation (MLE), namun hasilnya tidak closed-form sehingga diselesaikan dengan iterasi numerik. Iterasi numerik yang digunakan adalah iterasi BHHH. Statistik uji untuk pengujian serentak menggunakan Maximum Likelihood Ratio Test (MLRT). Hasil pemodelan menunjukkan bahwa pemodelan GTWBNBR exposure memberikan akurasi terbaik dibandingkan dengan pemodelan BNBR exposure. Pemodelan menggunakan GTWBNBR exposure menghasilkan beberapa kelompok kabupaten/kota berdasarkan variabel signifikan terhadap respon. Variabel signifikan yang berbeda-beda antar wilayah dan antar periode.
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Negative Binomial Regression (NBR) is an alternative modeling when the response is discrete and there is a violation of the equidispersion assumption. When there are two correlated count responses and there is a violation of the equidispersion assumption, then one of the appropriate models to use is Bivariate Negative Binomial Regression (BNBR). BNBR modeling was carried out with and without exposure variables. The BNBR model with variable exposure has the best accuracy with the smallest RMSE and the larger R2. This research examine a BNBR exposure method that accommodates spatial and temporal heterogeneity because the data used is in the form of a panel with an observation unit in the form of an area known as Geographically and Temporally Weighted Bivariate Negative Binomial Regression (GTWBNBR) with an exposure variable. The modeling is applied to cases of the number of maternal deaths and the number of infant deaths in Central Java Province in 2016-2020. The parameter estimation of the GTWBNBR exposure model uses Maximum Likelihood Estimation (MLE), but the results are not closed-form so it is solved by numerical iteration. The numerical iteration used is the BHHH iteration. Test statistics for simultaneous testing using the Maximum Likelihood Ratio Test (MLRT). The modeling results show that GTWBNBR exposure modeling provides the best accuracy compared to BNBR exposure modeling. Modeling using GTWBNBR exposure resulted in several groups of districts/cities based on significant variables in response. Significant variables that differ between regions and between periods.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | RTSt 519.536 Nin p-1 2022 |
| Uncontrolled Keywords: | GTWBNBR, Kematian Ibu, Kematian Bayi, MLE, MLRT, Variabel Exposure, Maternal Mortality, Infant Mortality, MLE, MLRT, Exposure Variabel. |
| Subjects: | Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Mr. Marsudiyana - |
| Date Deposited: | 30 Apr 2026 05:24 |
| Last Modified: | 30 Apr 2026 05:24 |
| URI: | http://repository.its.ac.id/id/eprint/132942 |
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