Penaksiran Parameter Dan Statistik Uji Dalammodel Regresi Geographically Weighted Poisson Inverse Gaussian (Studi Kasus Jumlah Kasus Baru HIV di Propinsi Jawa Timur Tahun 2013)

Purnamasari, Ima (2016) Penaksiran Parameter Dan Statistik Uji Dalammodel Regresi Geographically Weighted Poisson Inverse Gaussian (Studi Kasus Jumlah Kasus Baru HIV di Propinsi Jawa Timur Tahun 2013). Masters thesis, Institut Technology Sepuluh Nopember.

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Abstract

Regresi Poisson adalah salah satu anggota keluarga dari Generalized Linear Models (GLMs) yang berasal dari distribusi Poisson. Dalam distribusi Poisson terdapat asumsi yang harus terpenuhi yaitu mean dan varians variabel respon harus sama (equidispersion). Oleh karena itu, regresi Poisson Inverse Gaussian (PIG ) merupakan salah satu bentuk regresi yang dirancang untuk pemodelan data cacahan dengan kasus overdispersi. Pengembangan model regresi yang memperhatikan faktor heterogenitas spasial yaitu Geographically Weighted Regression (GWR). Selanjutnya variabel respon yang diteliti mengikuti distribusi PIG akan dikembangkan menjadi Geographically Weighted Poisson Inverse Gaussian Regression (GWPIGR). Penaksiran parameter menggunakan Maximum Likelihood Estimation (MLE) dan pengujian hipotesis dilakukan dengan Maximum Likelihood Ratio Test (MLRT). Pada penelitian analisis GWPIGR ini akan diterapkan pada jumlah kasus baru HIV di Propinsi Jawa Timur Tahun 2013 menggunakan 4 fungsi pembobot. Dari hasil analisis ini diketahui terdapat pembagian wilayah terhadap jumlah kasus baru HIV berdasarkan kesamaan variabel signifikan yang mempengaruhi yaitu 16 kelompok untuk Adaptive Bisquare, 27 kelompok untuk Fixed Bisquare, 27 kelompok untuk Fixed Gaussian, dan 28 kelompok untuk Adaptive Gaussian. Dan didapatkan model GWPIGR dengan pembobot Adaptive Bisquare merupakan model terbaik dengan 7 X (persentase penduduk usia 25-34 tahun) merupakan variabel yang sebagian besar berpengaruh. ============================================================================================================== Poisson regression is a member of Generalized Linear Models (GLMs) family which is derived from a Poisson distribution. Poisson distribution is only determined by one parameter that defines both the mean and variance of the distribution. In Poisson regression there is an assumption that must be complete, that are mean and variance of the response variable should be the same (equidispersion). Therefore, modeling the count data is not sufficient with a simple Poisson regression. Poisson Inverse Gaussian Regression (PIGR) is a regression which is derived from mixed Poisson distribution that is designed for count data modeling with overdispersion case. PIGR will produce global model that is assumed to be valid in all areas in which the data was taken. But of course every region has different geographical conditions, social, cultural and economic. Thus, the development of a regression model that considers spatial effect, which is Geographically Weighted Regression (GWR) needs to be employed. Furthermore, the response variable must follow the PIG distribution so development will be Geographically Weighted Poisson Inverse Gaussian Regression (GWPIGR). Parameter estimation is using Maximum Likelihood Estimation (MLE) and the statistical test using Miximum Likelihood Ratio Test (MLRT). In GWPIGR analysis research will be applied to the number of new HIV cases in East Java province in 2013 using four weighting function. From the analysis known that there is a territorial division of the amount of new cases of HIV based on common significant variable predictor there are 16 groups for Adaptive Bisquare, 27 groups for Fixed Bisquare, 27 groups for Fixed Gaussian, and 28 groups for Adaptive Gaussian. And obtained GWPIGR models with Adaptive Bisquare is the best model with 7 X (percentage of population aged 25-34 years) are variable that mostly influence.

Item Type: Thesis (Masters)
Additional Information: RTSt 519.536 Pur p
Uncontrolled Keywords: Regresi GWPIG, MLE, MLRT, HIV.
Subjects: Q Science > QA Mathematics > QA278.2 Regression Analysis
Divisions: Faculty of Mathematics and Science > Statistics > 49101-(S2) Master Thesis
Depositing User: Mr. Tondo Indra Nyata
Date Deposited: 22 Jan 2020 07:26
Last Modified: 22 Jan 2020 07:26
URI: http://repository.its.ac.id/id/eprint/72893

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