SETIAWAN, DEWI INDRA (2017) PENAKSIRAN PARAMETER DAN PENGUJIAN HIPOTESIS PADA GEOGRAPHICALLY WEIGHTED BIVARIATE GENERALIZED POISSON REGRESSION (Studi Kasus: Jumlah Kematian Bayi dan Jumlah Kematian Ibu di Jawa Timur tahun 2013). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Regresi poisson merupakan salah satu analisis regresi non linier yang variabel responnya mengikuti distribusi poisson. Pemodelan regresi poisson diperuntukkan hanya pada satu variabel respon disebut regresi univariat poisson, sedangkan pemodelan regresi poisson yang diperuntukkan pada dua variabel respon disebut regresi bivariat poisson. Model regresi poisson, baik regresi univariat poisson dan regresi bivariat poisson, memiliki asumsi spesifik, yaitu kesamaan antara rata-rata dan varians atau dikenal dengan istilah ekuidispersi. Apabila asumsi ini tidak terpenuhi akan menghasilkan kesimpulan yang tidak valid. Pelanggaran asumsi terjadi jika nilai rata-rata lebih besar daripada nilai varians (overdispersi). Regresi generalized poisson merupakan salah satu alternatif untuk mengatasi kasus overdispersi pada regresi Poisson. Bivariate Generalized Poisson Regression adalah pengembangan regresi bivariat poisson pada data yang mengalami kasus overdispersi. Pemodelan ini menghasilkan taksiran parameter yang bersifat global untuk seluruh lokasi (daerah). Adanya pengaruh lokasi yang merupakan faktor penting terhadap pemodelan apabila dilakukan di setiap daerah yang berbeda-beda.
Geographically Weighted Bivariat Generalized Poisson (GWBGPR) adalah regresi bivariat generalized poisson yang mempertimbangkan efek spasial dimana data tersebut diambil. Kematian bayi dan kematian ibu merupakan dua hal yang saling terkait erat karena selama dalam kandungan ibu, janin sangat tergantung pada gizi yang dikonsumsi oleh ibunya. Analisis yang digunakan untuk memodelkan jumlah kematian bayi dan jumlah kematian ibu serta faktor-faktor yang mempengaruhinya ditiap kab/kota di Jawa Timur adalah GWBGPR. Penaksiran parameter model GWBGPR menggunakan MLE dengan metode iterasi Newton Raphson dan pengujian hipotesis mengunakan MLRT. Metode GWBGPR menghasilkan parameter yang berbeda-beda pada setiap lokasi. Variabel prediktor yang berpengaruh signifikan terhadap jumlah kematian bayi dan jumlah kematian ibu adalah presentase persalinan oleh tenaga kesehatan, presentase ibu hamil mendapatkan tablet Fe3 dan presentase wanita kawin dengan tingkat pendidikan SD kebawah.
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Poisson Regression is one of the non-linear regression models in response variables follow the Poisson distribution. Poisson regression model that are appropriate for modeling one response called univariate poisson regression and poisson regression model that are appropriate for modeling paired count data exhibiting correlation called bivariate poisson regression model. Poisson regression model have a specific assumption, called equidispersion (equality of mean and variance), in practical applications and in “real” situations, this assumption is questionable since the variance can either be larger or smaller than the mean. If the variance is not equal to the mean, the estimation of poisson regression model are still consistent but inefficient, which leads to the invalidation of inference based on the estimated standard errors. Generalized poisson regression (GPR) has been found useful in fitting under-or overdispersed count data. Bivariate generalized poisson regression is a correlated bivariate version of the univariate generalized poisson regression. Parameter estimation of BGPR model produces a global model for each observation location. Interpretation of this global model assumes that each location has the same characteristics but in some cases each location has different characteristics. The characteristics of each region is very likely affect the number of events in the region as well as the incidence of the Poisson distribution. Bivariate Generalized Poisson Regression model that notice the presence of spatial effects in the data called Geographically Weighted Bivariate Generalized Poisson Regression (GWBGPR). Infant mortality and maternal mortality are correlated at each other because during pregnancy, the fetus depends on the nutrient that is consumed by the mother.
GWBGPR method will be applied for modelling maternal mortality and infant mortality in east java at 2013. Parameter estimation of GWBGPR model were done by using Maximum Likelihood Estimation (MLE) [4]. The parameter estimation of GWBGPR model using MLE method are not closed form so that the estimation process will be continued using newton raphson iteration. GWBGPR method produce local models to each observation location. Predictor that affected significantly to all groups for infant mortality and maternal mortality are percentage of deliveries by skilled health personnel, the percentage of pregnant women receiving tablets Fe3 and the percentage of married women with elementary education
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Overdispersi, Bivariat Generalized Poisson, GWBGPR, MLE, MLRT |
| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression |
| Divisions: | Faculty of Mathematics and Science > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | DEWI INDRA SETIAWAN |
| Date Deposited: | 23 Jan 2017 04:51 |
| Last Modified: | 05 Mar 2019 06:33 |
| URI: | http://repository.its.ac.id/id/eprint/2457 |
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