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.
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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. Logistic regression |
| 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: | 29 Apr 2024 01:56 |
| URI: | http://repository.its.ac.id/id/eprint/72903 |
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