Permodelan Geographically Weighted Gamma Regression Studi Kasus: Pencemaran Sungai Di Kota Surabaya Tahun 2013

Putri, Dina Eka (2016) Permodelan Geographically Weighted Gamma Regression Studi Kasus: Pencemaran Sungai Di Kota Surabaya Tahun 2013. Masters thesis, Institut Technology Sepuluh Nopember.

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Abstract

Regresi gamma merupakan regresi nonlinier untuk memodelkan hubungan antara satu atau lebih variabel prediktor dengan suatu variabel respons kontinu positif yang mengikuti distribusi gamma. Regresi gamma menghasilkan parameter bersifat global yang dianggap valid di setiap lokasi. Pada kenyataannya, setiap lokasi dapat memiliki karakteristik yang berbeda sehingga adanya pengaruh spasial perlu dipertimbangkan. Oleh karena itu diperlukan pendekatan dengan Geographically Weighted Gamma Regression (GWGR). Studi kasus yang digunakan pada penelitian ini adalah pencemaran sungai di kota Surabaya dengan indikator pencemaran, yaitu Biological Oxygen Demand (BOD). Penelitian ini bertujuan untuk mengestimasi parameter, mendapatkan uji statistik, dan faktor-faktor yang berpengaruh terhadap kadar BOD sungai-sungai di kota Surabaya berdasarkan model GWGR. Estimasi parameter dilakukan dengan Maximum Likelihood Estimation (MLE) dengan metode optimasi menggunakan algoritma Broyden-Fletcher-Goldfarb-Shanno (BFGS). Pengujian hipotesis dilakukan secara parsial menggunakan uji Z, sedangkan secara simultan menggunakan Maximum Likelihood Ratio Test (MLRT). Faktor-faktor yang berpengaruh terhadap kadar BOD adalah kedalaman, kecepatan aliran air, fosfat, dan amonia. =============================================================================================================== Gamma regression is a nonlinear regression used to model relationship between one or more independent variables and a positive continuous dependent variable that follows gamma distribution. Having applied to observations from different location, the gamma regression yields parameters which are assumed to be valid in any location. In fact, each location may have different characteristics such that the existence of spatial effect needs to be considered. Thus, Geographically Weighted Gamma Regression (GWGR) plays into role. GWGR is a local form of gamma regression that considers the spatial effect. This study aims to estimate parameters of GWGR model using Maximum Likelihood Estimation (MLE) method along with to test the significance of those estimated parameters and to determine which factors Biological Oxygen Demand (BOD) level in Surabaya based on GWGR model. As the MLE method could not produce solution analytically, a numerical optimization method using Broyden-Fletcher- Goldfarb-Shanno (BFGS) algorithm was employed to estimate the parameters. Hypothesis testing procedure was used to test the significance of independent variables within the model, both partially using Z-test and simultaneously using Maximum Likelihood Ratio Test (MLRT). Generally, factors affecting BOD level were depth of the river, water flow rate, phosphate, and ammonia.

Item Type: Thesis (Masters)
Additional Information: RTSt 519.536 Put p
Uncontrolled Keywords: Regresi gamma, geographically weighted gamma regression, algoritma BFGS, Maximum Likelihood Ratio Test
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 08:19
Last Modified: 22 Jan 2020 08:19
URI: http://repository.its.ac.id/id/eprint/72903

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