Sari, Meylita (2021) Geographically and Temporally Weighted Bivariate Poisson Inverse Gaussian Regression Model (Studi Kasus : Pemodelan Penambahan Kasus Covid-19 dan Penambahan Kematian Akibat Covid-19 di Jawa Timur). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Distribusi Poisson merupakan distribusi diskrit dengan variabel random berupa data cacahan (count). Pada regresi Poisson terdapat asumsi yang harus terpenuhi yaitu mean dan variansi variabel respon harus sama (equidispersi). Namun dalam kenyataannya sering kali terjadi pelanggaran asumsi yaitu underdispersi atau overdispersi. Kasus overdispersi diatasi dengan pemodelan yang terdiri dari gabungan distribusi Poisson dengan distribusi lain, salah satunya yaitu distribusi Poisson Inverse Gaussian (PIG). Regresi bivariate PIG (BPIG) adalah regresi mixed Poisson untuk pemodelan data count berpasangan yang mengalami overdispersi. Penambahan kasus baru COVID-19 dan penambahan kematian akibat COVID-19 merupakan contoh data count berpasangan. Provinsi Jawa Timur merupakan wilayah yang tergolong tinggi kasus COVID-19 dan sangat mengkhawatirkan karena mengalami peningkatan yang signifikan pada penambahan kasus COVID-19 dan penambahan kematian akibat COVID-19. Oleh karena itu, untuk melihat faktor-faktor yang mempengaruhi penambahan kasus COVID-19 dan penambahan kematian COVID-19 dilakukan pengembangan model regresi yang memperhatikan faktor pembobot geografis dan temporal sehingga memberikan model lokal yang berbeda-beda di setiap lokasi dan waktu. Perbedaan ini dipengaruhi oleh beberapa faktor seperti keadaan geografis, sosial, kebudayaan, ekonomi dan lain-lain. Model Geographically and Temporally Weighted Bivariate Poisson Inverse Gaussian Regression (GTWBPIGR) digunakan untuk mengatasi kasus overdispersi dan membentuk model lokal yang dipengaruhi efek spasial dan temporal. Metode penaksiran parameter menggunakan Maximum Likelihood Estimation (MLE) dengan algoritma Newton-Raphson. Pengujian hipotesis menggunakan metode Maximum Likelihood Ratio Test (MLRT). Hasil pemodelan menggunakan metode GTWBPIGR menghasilkan bahwa faktor yang berpengaruh signifikan terhadap penambahan kasus COVID-19 dan penambahan kematian akibat COVID-19 di tiap daerah dan periode saling berbeda. Tiap daerah pada tiap periode minimal memiliki dua faktor yang berpengaruh signifikan terhadap penambahan kasus COVID-19 dan penambahan kematian akibat COVID-19 yaitu rata-rata suhu dan rata-rata kelembaban.
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Poisson distribution is a discrete distribution with a random variable in the form of count data. In Poisson regression, some assumptions must be fulfilled: the mean and variance of the response variables must be the same (equidispersion). However, in reality, there is often a violation of assumptions, namely underdispersion or over-dispersion. The overdispersion case is handled by modelling, which consists of combining the Poisson distribution with other distributions, one of which is the Poisson Inverse Gaussian (PIG) distribution. Bivariate PIG Regression (BPIGR) is a mixed Poisson regression for modelling overdispersion of paired count data. The addition of cases of COVID-19 and death cases due to COVID-19 are examples of paired count data East Java Province is a region classified as high COVID-19 cases and very worrying because it has experienced a significant increase in the addition of COVID-19 cases and additional cases of death due to COVID-19. Therefore, to see the factors that influence COVID-19 cases and additional COVID-19 death cases, a regression model is developed that considers geographic and temporal weighting factors to provide different local models in each location and time. This difference is influenced by several factors such as geographical, social, cultural, economic conditions and others. Geographically Temporally Weighted Bivariate Poisson Inverse Gaussian Regression (GTWBPIGR) model is used to overcome overdispersion cases and form a local model influenced by geography and temporal aspects. The method of parameter estimation uses the Maximum Likelihood Estimation (MLE) with the Newton-Raphson algorithm. Hypothesis testing uses the Maximum Likelihood Ratio Test (MLRT) method. The results of modeling using the GTWBPIGR method show that the factors that have a significant effect on the addition of COVID-19 cases and the addition of deaths due to COVID-19 in each region and period are different. Each region in each period has at least two factors that have a significant effect on the addition of COVID-19 cases and the increase in deaths due to COVID-19 namely the variables of average temperature and average relative humidity.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | GTWBPIGR, MLE, MLRT, Penambahan kasus COVID-19, Penambahan Kematian akibat COVID-19 di Jawa Timur COVID-19 Cases and Deaths cases due to COVID-19 in East Java, GTWBPIGR, MLE, MLRT |
| Subjects: | H Social Sciences > HA Statistics > HA30.6 Spatial analysis Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Meylita Sari |
| Date Deposited: | 09 Sep 2021 07:18 |
| Last Modified: | 09 Sep 2021 07:18 |
| URI: | http://repository.its.ac.id/id/eprint/91909 |
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