Ramadany, Rizqiyanti (2021) Penaksiran Parameter dan Pengujian Hipotesis Model Multivariate Adaptive Bivariate Generalized Poisson Regression Spline (Studi Tentang: Jumlah Kasus dan Jumlah Kematian Covid-19 di Pulau Jawa). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Regresi Poisson merupakan regresi yang digunakan untuk memodelkan data
count. Variabel respon regresi Poisson mengikuti distribusi Poisson. Regresi
Poisson memiliki asumsi khusus yaitu nilai rata-rata variabel respon sama dengan
nilai ragam variabel respon atau yang dikenal dengan asumsi ekuidispersi. Apabila
asumsi ekuidispersi tidak bisa terpenuhi dapat menggunakan metode Generalized
Poisson Regression (GPR). Multivariate Adaptive Regression Spline (MARS)
adalah suatu metode nonparametrik dengan keunggulan mampu mengatasi
permasalahan data dengan banyak variabel prediktor 3 ≤ p ≤ 20
Apabila terdapat
dua variabel respon yang saling berkorelasi, maka model yang digunakan adalah
pengembangan gabungan model MARS dan BGPR menjadi suatu model
Multivariate Adaptive Bivariate Generalized Poisson Regression Spline
(MABGPRS). Hasil penelitian menunjukkan bahwa penaksiran parameter model
MABGPRS menggunakan metode Weighted Least Square (WLS) dan Maximum
Likelihood Estimation (MLE). Statistik uji untuk pengujian serentak menggunakan
Maximum Likelihood Ratio Test (MLRT). Model MABGPRS diterapkan pada
jumlah kasus dan jumlah kematian Covid-19 di Pulau Jawa tahun 2020. Unit
penelitiannya adalah 119 Kabupaten/Kota di Pulau Jawa. Variabel prediktor yang
digunakan sebanyak tujuh variabel. Seluruh variabel prediktor berpengaruh
terhadap jumlah kematian Covid-19 di Pulau Jawa. Variabel prediktor yang
berpengaruh terhadap jumlah kasus Covid-19 di Pulau Jawa adalah sebanyak enam
variabel prediktor. Variabel angka kesakitan/morbiditas tidak berkonstribusi
terhadap pembentukan model MABGPRS jumlah kasus Covid-19 di Pulau Jawa.
Berdasarkan nilai kepentingan variabel diketahui bahwa kepadatan penduduk (X1)
dan persentase rumah tangga dengan sumber air minum layak (X4) adalah variabel
terpenting pada model MABGPRS jumlah kasus Covid-19 dengan nilai tingkat
kepentingan variabel 100. Variabel terpenting pada model MABGPRS jumlah
kematian Covid-19 adalah persentase rumah tangga dengan akses sanitasi layak
(X3) dan kelembaban udara (X7) dengan nilai tingkat kepentingan variabel 100.
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Poisson regression is a regression used to model count data. The Poisson
regression response variable follows the Poisson distribution. Poisson regression
has a special assumption, namely the average value of the response variable is equal
to the value of the variance of the response variable, which is known as the
assumption of equidispersion. If the assumption of equidispersion cannot be met,
the Generalized Poisson Regression (GPR) method can be used. Multivariate
Adaptive Regression Spline (MARS) is a nonparametric method with the advantage
of being able to overcome data problems with many predictor variables 3 ≤ 20. If
there are two response variables that are correlated with each other, the model used
is the combined development of the MARS and BGPR models into a model.
Multivariate Adaptive Bivariate Generalized Poisson Regression Spline
(MABGPRS). The results showed that the parameter estimation of the MABGPRS
model used the Weighted Least Square (WLS) and Maximum Likelihood
Estimation (MLE) methods. Test statistics for simultaneous testing using the
Maximum Likelihood Ratio Test (MLRT). The MABGPRS model is applied to the
number of cases and the number of deaths of Covid-19 on the island of Java in
2020. The research unit is 119 districts/cities on the island of Java. The predictor
variables used were seven variables. All predictor variables affect the number of
Covid-19 deaths in Java. The predictor variables that affect the number of Covid�19 cases in Java are six predictor variables. The variable percentage of the
population who has health complaints/morbidities has no contribution on the
MABGPRS model of thwnumber of Covid-19 cases in Java. Based on the value of
the variable importance, it is known that population density (X1) and the percentage
of households with adequate drinking water sources (X4) are the most important
variables in the MABGPRS model the number of Covid-19 cases with a variable
importance value of 100. The most important variable in the MABGPRS model is
the number of Covid-19 deaths. 19 is the percentage of households with access to
proper sanitation (X3) and humidity (X7) with a variable importance value of 100.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | BGPR, MABGPRS, Jumlah Kasus Covid-19, Jumlah Kematian Covid-19, MARS, MLE, MLRT, WLS, BGPR, MABGPRS, MARS, MLE, MLRT, Number of Covid-19 Cases, Number of Covid-19 Deaths, WLS |
| Subjects: | Q Science > QA Mathematics > QA371 Differential equations--Numerical solutions Q Science > QA Mathematics > QA278 Cluster Analysis. Multivariate analysis. Correspondence analysis (Statistics) |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | Rizqiyanti Ramadany |
| Date Deposited: | 10 Sep 2021 09:24 |
| Last Modified: | 26 Jul 2024 07:00 |
| URI: | http://repository.its.ac.id/id/eprint/91965 |
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