Penaksiran Parameter dan Pengujian Hipotesis pada Model Geographically Weighted Bivariate Poisson Inverse Gaussian Regression (Studi Kasus: Jumlah Kasus Baru Kusta PB dan Kusta MB di Provinsi Sumatera Barat Tahun 2014)

Amalia, Junita (2018) Penaksiran Parameter dan Pengujian Hipotesis pada Model Geographically Weighted Bivariate Poisson Inverse Gaussian Regression (Studi Kasus: Jumlah Kasus Baru Kusta PB dan Kusta MB di Provinsi Sumatera Barat Tahun 2014). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Distribusi Poisson merupakan distribusi diskrit dengan variabel random berupa data count. Pada regresi Poisson terdapat asumsi yang harus terpenuhi yaitu mean dan varians variabel respon harus sama (equidispersi). Namun dalam kenyataannya sering terjadi pelanggaran asumsi yaitu underdispersi atau over-dispersi. Kasus overdispersi diatasi dengan pemodelan yang terdiri dari gabungan distribusi Poisson dengan distribusi lain, baik distribusi diskrit maupun kontinyu (mixed poisson distribution). Bivariate Poisson Inverse Gaussian Regression (BPIGR) adalah regresi mixed poisson untuk pemodelan data count berpasangan yang mengalami overdispersi. Provinsi Sumatera Barat merupakan wilayah dengan kasus kusta yang tergolong rendah, namun sangat menghawatirkan karena mengalami peningkatan yang signifikan. Untuk melihat faktor-faktor yang mempengaruhi jumlah kasus baru kusta PB dan kusta MB di Sumatera Barat dilakukan pengembangan model regresi yang memperhatikan faktor pembobot geografis sehingga memberikan model lokal yang berbeda-beda di setiap lokasi. Perbedaan ini dipengaruhi oleh beberapa faktor seperti keadaan geografis, sosial, kebudayaan, ekonomi dan lain-lain. Model Geographically Weighted Bivariate Poisson Inverse Gaussian Regression (GWBPIGR) digunakan untuk mengatasi kasus overdispersi dan membentuk model lokal. Metode penaksiran parameter menggunakan Maximum Likelihood Estimation (MLE) dengan algoritma Newton-Raphson. Pengujian hipotesis menggunakan metode Maximum Likelihood Ratio Test (MLRT). Untuk setiap kabupaten/kota di Sumatera Barat memiliki nilai taksiran parameter yang berbeda-beda sehingga menghasilkan model lokal. Variabel penjelas yang digunakan adalah persentase rumah sehat, persentase penduduk miskin, persentase tempat pengelolaan makana (TPM) menurut status higenie sanitasi sehat dan rasio tenaga medis. Hampir semua variabel berpengaruh secara signifikan untuk setiap kabupaten/kota, kecuali di kabupaten Solok Selatan dan kabupaten Sinjunjung variabel persentase TPM menurut status higenie sanitasi sehat tidak berpengaruh signifikan. ============== Poisson distribution is a discrete distribution with count data as the random variables and it has one parameter defines both mean and variance. Poisson regression assumes mean and variance should be same (equidispersion). Nonetheless, some case of the count data unsatisfied this assumption because variance exceeds mean (overdispersion). Overdispersion case is overcome by forming some modelling which is combination of Poisson distribution with several distribution either discrete or continuous (mixed Poisson distribution). Bivariate Poisson Inverse Gaussian Regression (BPIGR) model is mixed Poisson regression for modeling paired count data within overdispersion. West Sumatera is a region with low leprosy cases, but it is worrying because it has a significant increse. The number of PB and MB leprosy in West Sumatera is one of count data within overdispersion so can modelling by BPIGR. To see the factors affecting the number of new cases of PB and MB leprosy in West Sumatera in this study will be develop a regression model that has geographic weighting factors, which will provide different local models in each location. This difference is influenced by several factors such as geographic conditions, social, culture, economic and so on. Geographically Weighted Bivariate Poisson Inverse Gaussian Regression (GWBPIGR) model is used to solve overdispersion and to generate local models. Parameter estimation obtained by Maximum Likelihood Estimation (MLE) method with Newton-Raphson algorithm. Meanwhile hypothesis testing acquired by Maximum Likelihood Ratio Test (MLRT) method. For each district/city in West Sumatera has different parameter so produce different local model. The explanatory variables that influence are percentage of healthy house, percentage of poor people, percentage of food management places according to hygiene sanitation status and ratio of medical personnel. Almost all of variables significantly influence for each district/city, except in South Solok district and Sinjunjung district the percentage of food management places according to higenie sanitation status has no significant effect.

Item Type: Thesis (Masters)
Uncontrolled Keywords: Geographically Weighted Bivariate Poisson Inverse Gaussian Regression (GWBPIGR); Kusta PB dan Kusta MB di Sumatera Barat tahun 2014; Geographically Weighted Bivariat e Poisson Inverse Gaussian Regression (GWBPIGR); PB and MB leprosy in West Sumatra 2014.
Subjects: Q Science > QA Mathematics > QA278.2 Regression Analysis
Divisions: Faculty of Mathematics and Science > Statistics > (S2) Master Theses
Depositing User: Amalia Junita
Date Deposited: 06 Mar 2018 04:22
Last Modified: 06 Mar 2018 04:22
URI: http://repository.its.ac.id/id/eprint/50385

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