Islamiati, Mawadah Putri (2025) Model Mixed Geographically Weighted Bivariate Zero-Inflated Negative Binomial Regression (Studi Kasus: Jumlah Kematian Ibu Nifas dan Post Neonatal di Kabupaten Sukabumi 2023). Masters thesis, Institut Teknologi Sepuluh Nopember.
![[thumbnail of 6003231025-Master_Thesis.pdf]](http://repository.its.ac.id/style/images/fileicons/text.png) |
Text
6003231025-Master_Thesis.pdf - Accepted Version Restricted to Repository staff only Download (9MB) | Request a copy |
Abstract
Distribusi Bivariate Zero-Inflated Negative Binomial (BZINBR) merupakan distribusi mixed Poisson yang dirancang untuk menangani dua variabel random berupa data cacahan yang saling berkorelasi serta mengalami overdispersi akibat tingginya presentase excess zeros. Pengembangan dari distribusi BZINBR yang mempertimbangkan heterogenitas spasial menghasilkan model Geographically Weighted Bivariate Zero-Inflated Negative Binomial Regression (GWBZINBR). Namun, tidak semua variabel prediktor dalam model GWBZINBR memberikan pengaruh secara lokal; beberapa justru bersifat global. Oleh karena itu, GWBZINBR dikembangkan menjadi Mixed Geographically Weighted BZINBR (MGWBZINBR) yang mengakomodasi kombinasi efek lokal dan global. Penelitian ini membahas kajian teori terhadap estimasi parameter dan pengujian hipotesis dalam model MGWBZINBR. Estimasi dilakukan menggunakan Maximum Likelihood Estimation (MLE), di mana fungsi likelihood tidak berbentuk closed- form sehingga diperlukan optimasi nonlinier dengan algoritma iteratif Berndt, Hall, Hall, dan Hausman (BHHH). Model MGWBZINBR kemudian diterapkan pada data jumlah kematian ibu nifas dan kematian post neonatal di 47 kecamatan di Kabupaten Sukabumi tahun 2023 untuk mengidentifikasi faktor-faktor yang memengaruhinya. Hasil pengelompokan menunjukkan bahwa pada variabel respon kematian ibu nifas (Y₁), terdapat 32 kombinasi variabel signifikan yang membentuk kelompok wilayah dengan karakteristik berbeda, menunjukkan heterogenitas spasial yang tinggi. Sementara itu, pada kematian post neonatal (Y₂), ditemukan 23 kombinasi yang lebih seragam antar kecamatan, dengan dominasi variabel X₄ (penanganan komplikasi kebidanan) dan X₅ (rasio bidan). Model MGWBZINBR terbukti sebagai model terbaik karena mampu menangkap variasi pengaruh lokal dan global secara simultan, memberikan interpretasi yang lebih akurat, serta menghasilkan nilai AICc terkecil dibandingkan model global maupun spasial sebelumnya.
===============================================================================================================================
The Bivariate Zero-Inflated Negative Binomial (BZINBR) distribution is a mixed Poisson distribution designed to model two correlated count variables that exhibit overdispersion due to a high proportion of excess zeros. An extension of BZINBR that accounts for spatial heterogeneity is known as the Geographically Weighted Bivariate Zero-Inflated Negative Binomial Regression (GWBZINBR). However, not all predictor variables in GWBZINBR exert purely local effects; some behave globally. Therefore, the model is further developed into the Mixed Geographically Weighted BZINBR (MGWBZINBR), which accommodates both local and global effects simultaneously. This study discusses the theoretical framework for parameter estimation and hypothesis testing in the MGWBZINBR model. Parameter estimation is performed using Maximum Likelihood Estimation (MLE), where the likelihood function is not in closed form and thus requires nonlinear optimization through the iterative Berndt, Hall, Hall, and Hausman (BHHH) algorithm. The MGWBZINBR model is then applied to data on maternal and post-neonatal mortality from 47 subdistricts in Sukabumi Regency in 2023, with the aim of identifying influencing factors. The grouping results show that for maternal mortality (Y₁), there are 32 different combinations of significant predictors across regions, indicating a high degree of spatial heterogeneity. In contrast, post-neonatal mortality (Y₂) exhibits 23 more homogeneous combinations, predominantly influenced by variables X₄ (management of obstetric complications) and X₅ (midwife ratio). MGWBZINBR is proven to be the best model, as it captures both local and global variation simultaneously, provides more accurate interpretation, and yields the lowest AICc value compared to previous global and spatial models.
Actions (login required)
 |
View Item |