Geographically and Temporally Weighted Bivariate Gamma Regression Model (Studi Kasus: Angka Partisipasi Kasar dan Angka Partisipasi Murni SMA/Sederajat di Provinsi Sulawesi Selatan)

Wasani, Desy (2021) Geographically and Temporally Weighted Bivariate Gamma Regression Model (Studi Kasus: Angka Partisipasi Kasar dan Angka Partisipasi Murni SMA/Sederajat di Provinsi Sulawesi Selatan). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Banyak bidang penelitian menggunakan data spasial. Model Geographically Weighted Bivariate Gamma Regression (GWBGR) menangani adanya efek spasial yang berupa heterogenitas spasial pada regresi bivariat dengan variabel respon berdistribusi gamma. Dalam perkembangannya, banyak kasus yang membutuhkan informasi dari data panel. Penggunaan data panel dapat memberikan informasi yang lebih lengkap karena mencakup beberapa periode, tetapi memungkinkan adanya efek temporal. Penelitian ini mengembangkan model Geographically and Temporally Weighted Bivariate Gamma Regression (GTWBGR) untuk menangani heterogenitas spasial dan temporal secara bersamaan. Pemodelan GTWBGR dilakukan pada Angka Partisipasi Kasar (APK) dan Angka Partisipasi Murni (APM) SMA/sederajat di Provinsi Sulawesi Selatan tahun 2015-2019 untuk mendapatkan faktor-faktor yang berpengaruh. Penaksiran parameter model menggunakan metode Maximum Likelihood Estimation (MLE) menunjukkan hasil yang tidak closed-form, sehingga dilanjutkan dengan iterasi numerik Berndt-Hall-Hall-Hausman (BHHH). Pengujian hipotesis serentak menggunakan metode Maximum Likelihood Ratio Test (MLRT). Pengujian parsial di 24 lokasi kabupaten/kota dan 5 periode menunjukkan hasil signifikansi variabel prediktor yang berbeda-beda dan dapat dikelompokkan menjadi 4 kelompok kabupaten/kota. Variabel PDRB per kapita, kemiskinan, dan rasio jenis kelamin berpengaruh signifikan terhadap APK dan APM secara global di semua lokasi dan periode. Sementara itu, persentase anggaran pendidikan dan rasio murid-sekolah memiliki signifikansi yang bervariasi antar lokasi dan periode. Kebaikan model diukur dengan Sum of Squared Errors (SSE). Pemodelan pada periode 1, 2, dan 3 menggunakan semua data sampai dengan periode tersebut. Namun pada periode ke-4 dan ke-5 hanya menggunakan data sebanyak 3 periode sampai dengan periode tersebut dikarenakan merupakan model dengan nilai SSE terkecil.
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Many research fields use spatial data. The Geographically Weighted Bivariate Gamma Regression (GWBGR) model handles the spatial effect in the form of spatial heterogeneity in bivariate regression with the response variable being gamma-distributed. In its development, many cases require information from panel data. The use of panel data can provide more complete information because it covers several periods, but allows for a temporal effect. This study developed a Geographically and Temporally Weighted Bivariate Gamma Regression (GTWBGR) model to deal with spatial and temporal heterogeneity simultaneously. GTWBGR modeling was carried out on the Gross Enrollment Rate (GER) and Net Enrollment Rate (NER) for high school levels in South Sulawesi Province in 2015-2019 to obtain the influencing factors. The estimation of model parameters using the Maximum Likelihood Estimation (MLE) method showed results that were not closed-form, so that it was continued with the Berndt-Hall-Hall-Hausman (BHHH) numerical iteration. Simultaneous hypothesis testing used the Maximum Likelihood Ratio Test (MLRT) method. Partial testing in 24 districts/cities and 5 periods showed different significance of predictor variables and could be grouped into 4 groups of districts/cities. The variables GRDP per capita, poverty, and sex ratio have the significant effects on GER and NER globally in all locations and periods. Meanwhile, the significance of the percentage of the education budget and the student-school ratio varies among locations and periods. The goodness of the model is measured using the Sum of Squared Errors (SSE). Modeling in periods 1, 2, and 3 use all data up to that period. However, in periods 4 and 5, only 3 periods of data were used up to that period because it is the model with the smallest SSE value.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Angka Partisipasi Kasar, Angka Partisipasi Murni, GTWBGR, MLE, MLRT, Gross Enrollment Rate, Net Enrollment Rate, GTWBGR, 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:	Desy Wasani
Date Deposited:	09 Sep 2021 08:57
Last Modified:	09 Sep 2021 08:57
URI:	http://repository.its.ac.id/id/eprint/91937

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