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.
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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. Logistic regression |
| 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: | 24 May 2021 02:07 |
| URI: | http://repository.its.ac.id/id/eprint/72893 |
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