Model Multivariate Adaptive Geographically Weighted Generalized Poisson Regression Splines (Magwgprs) (Studi Kasus: Pemodelan Banyaknya Kasus Demam Berdarah Dengue)

Sriningsih, Riry (2023) Model Multivariate Adaptive Geographically Weighted Generalized Poisson Regression Splines (Magwgprs) (Studi Kasus: Pemodelan Banyaknya Kasus Demam Berdarah Dengue). Doctoral thesis, Institut Teknologi Sepuluh Nopember.

Text 06211960010011-Dissertation.pdf - Accepted Version Restricted to Repository staff only until 1 September 2025. Download (15MB) | Request a copy

Abstract

Multivariate Adaptive Generalized Poisson Regression Splines (MAGPRS) merupakan kombinasi antara Multivariate Adaptive Regression Splines (MARS) dan Generalized Poisson Regression (GPR). MAGPRS merupakan model MARS dengan respon count yang mampu mengatasi masalah equidispersion. Namun, model MAGPRS belum mempertimbangkan efek spasial pada data. Banyak kasus yang berkaitan dengan efek spasial (kewilayahan), diantaranya persebaran penyakit menular yang berbeda antar wilayah pengamatan. Perbedaan tersebut terjadi karena adanya perbedaan karakteristik antar lokasi pengamatan, yaitu perbedaan sosial ekonomi, kepadatan penduduk, tingkat pendidikan, kondisi lingkungan, dan sebagainya. Salah satu efek spasial ini adalah heterogenitas spasial (terjadinya pelanggaran asumsi homogenitas spasial). Tujuan penelitian ini adalah mengembangkan MAGPRS yang memperhatikan heterogenitas spasial, diberi nama dengan Multivariate Adaptive Geographically Weighted Generalized Poisson Regression Splines (MAGWGPRS). Model MAGWGPRS dibentuk berdasarkan fungsi basis MAPRS. Model tersebut dianalisis untuk mendapatkan penaksir parameter dan statistik uji hipotesis model. Penaksir parameter model menggunakan metode Maximum Likelihood Estimation (MLE) terboboti dengan metode iterasi Berndt-Hall-Hall-Hausman (BHHH). Pengujian hipotesis parameter model secara serentak dilakukan dengan Maximum Likelihood Ratio Test (MLRT) dan secara parsial dengan uji Wald. Tujuan berikutnya menerapkan model MAGWGPRS terhadap banyaknya kasus demam berdarah dengue (DBD) di kabupaten/kota Pulau Jawa. Berdasarkan kombinasi BF, MI, dan MO, dipilih satu model MAPRS terbaik dan satu model MAPRS lainnya yang fungsi basisnya berturut-turut dijadikan sebagai fungsi basis MAGWGPRS 1 dan MAGWGPRS 2. Hasil penelitian menunjukkan bahwa penaksir parameter kedua model tidak closed form dan diselesaikan secara numerik menggunakan metode BHHH. Masing-masing model MAGWGPRS 1 dan MAGWGPRS 2 juga menghasilkan fungsi basis yang berpengaruh signifikan berbeda untuk setiap kabupaten/kota di Jawa. Model MAGWGPRS 1 lebih menggambarkan heterogenitas spasial dibandingkan dengan model MAGWGPRS 2. Berdasarkan jumlah fungsi basisnya, model MAGWGPRS 1 memiliki 23 fungsi basis dan model MAGWGPRS 2 memiliki 11 fungsi basis. Berdasarkan nilai Mean of Square Error (MSE), model MAGWGPRS 1 lebih baik dibandingkan model MAGWGPRS 2 dalam memodelkan banyaknya kasus DBD di kabupaten/kota di Pulau Jawa pada tahun 2020.
=====================================================================================================================================
Multivariate Adaptive Generalized Poisson Regression Splines (MAGPRS) is a combination of Multivariate Adaptive Regression Splines (MARS) and Generalized Poisson Regression (GPR). MAGPRS is a MARS model with a count response that can overcome the problem of equidispersion. However, the MAGPRS model has not considered spatial effects on the data. Many cases are related to spatial effects, including the distribution of infectious diseases that differ between observation areas. This difference occurs due to differences in characteristics between observation locations, namely socio-economic differences, population density, education levels, environmental conditions, and so on. One of these spatial effects is spatial heterogeneity (violation of the assumption of spatial homogeneity). The purpose of this research is to develop MAGPRS that takes into account spatial heterogeneity, named Multivariate Adaptive Geographically Weighted Generalized Poisson Regression Splines (MAGWGPRS). The MAGWGPRS model is formed based on the MAPRS basis function. The model was analyzed to obtain parameter estimators and model hypothesis test statistics. The model parameter estimator uses the Maximum Likelihood Estimation (MLE) method and the Berndt-Hall-Hausman (BHHH) iteration method. Hypothesis testing of model parameters simultaneously is done with the Maximum Likelihood Ratio Test (MLRT) and partially with the Wald test. The next objective is to apply the MAGWGPRS model to the number of dengue hemorrhagic fever (DHF) cases in the districts/cities of Java Island. Based on the combination of BF, MI, and MO, one best MAPRS model and one other MAPRS model were selected whose basis functions were used as MAGWGPRS 1 and MAGWGPRS 2 basis functions, respectively. The results showed that the parameter estimators of the two models were not closed form and were solved numerically using the BHHH method. Each of the MAGWGPRS 1 and MAGWGPRS 2 models also produced significantly different basis functions for each district/city in Java. Based on the number of basis functions, the MAGWGPRS 1 model has 23 basis functions and the MAGWGPRS 2 model has 11 basis functions. Based on the Mean of Square Error (MSE) value, the MAGWGPRS 1 model is better than the MAGWGPRS 2 model in modeling the number of dengue cases in districts/cities in Java in 2020.

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	GPR, GWGPR, iterasi BHHH, MAGPRS, MAGWGPRS, MAPRS, MARS, MLE, MLRT; GPR, GWGPR, BHHH iteration, MAGPRS, MAGWGPRS, MAPRS, MARS, MLE, MLRT.
Subjects:	H Social Sciences > HA Statistics > HA30.6 Spatial analysis
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User:	Riry Sriningsih
Date Deposited:	21 Aug 2023 08:34
Last Modified:	21 Aug 2023 08:34
URI:	http://repository.its.ac.id/id/eprint/104827

Actions (login required)

View Item