Model Geographically and Temporally Weighted Multivariate Generalized Gamma Regression

Yasin, Hasbi (2025) Model Geographically and Temporally Weighted Multivariate Generalized Gamma Regression. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Distribusi Generalized Gamma merupakan bentuk umum dari distribusi gamma dengan penambahan satu parameter bentuk. Distribusi ini mampu mengenali data dari beberapa distribusi khusus, seperti Gamma, Weibull, Chi-kuadrat, Exponential, Rayleigh dan Half-Normal. Kajian model regresi menggunakan respon berdistribusi Generalized Gamma masih tebatas pada model-model regresi dari beberapa distribusi khusus tersebut. Penelitian ini mengembangkan Model Generalized Gamma Regression (GGR) untuk respon univariate maupun multivariate. Model GGR kemudian dikembangkan menjadi model Geographically and Temporally Weighted Multivariate Generalized Gamma Regression (GTWMGGR) dengan melibatkan unsur spasial dan periode temporal pengamatan. Tujuan penelitian ini adalah mendapatkan penaksir parameter, statistik uji, dan pengujian hipotesis parameter model GTWMGGR. Penaksiran parameter model dilakukan menggunakan metode Maximum Likelihood Estimation (MLE) yang kemudian dioptimasi menggunakan metode iterasi dengan algoritma Berndt-Hall-Hall-Hausman (BHHH). Pengujian parameter model secara serentak menggunakan Maximum Likelihood Ratio Test (MLRT) dan pengujian secara parsial menggunakan uji Wald. Model yang dikembangkan diaplikasikan pada pemodelan data indikator kinerja pendidikan dengan variabel respon Rata-rata Lama Sekolah (RLS), Angka Partisipasi Sekolah (APS) uisa 16-18 Tahun, dan Angka Partisipasi Kasar (APK) SMA/sederajat Kabupaten/Kota di Jawa Tengah selama periode tahun 2017 sampai dengan 2021. Sedangkan variabel prediktor yang digunakan adalah PDRB per Kapita, Persentase Penduduk Miskin, Rasio Jenis Kelamin, Persentase Rumah Tangga yang Memiliki Akses Terhadap Sanitasi Layak, Tingkat Partisipasi Angkatan Kerja (TPAK), dan Rasio Murid terhadap Guru SMP. Hasil pemodelan MGGR menunjukkan bahwa semua variabel prediktor secara serentak berpengaruh signifikan terhadap variabel respon. Sementara itu, model GTWMGGR menghasilkan variabel prediktor yang berpengaruh signifikan berbeda untuk masing-masing kabupaten/kota di Jawa Tengah. Model GTWMGGR menghasilkan akurasi terbaik karena mengakomodasi efek heterogenitas spatio-temporal.
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The Generalized Gamma distribution is a more general form of a Gamma distribution with an addition of one shape parameter. This distribution is able to recognize data from several other distributions, such as Gamma, Weibull, Chi-Square, Exponential, Rayleigh, and Half-Normal. The study of regression models using Generalized Gamma responses is still limited to regression models from such specific distributions. This research develops the Generalized Gamma Regression (GGR) model for univariate and multivariate responses. The GGR model is also developed to account the effect of the spatial and temporal heterogeneity, named Geographically and Temporally Weighted Multivariate Generalized Gamma Regression (GTWMGGR) model. This study aims to derive the procedure for parameter estimation and hypothesis testing of GTWMGGR model. The estimation of model parameters is developed using the Maximum Likelihood Estimation (MLE) method, which is then optimized using the numerical method with the Berndt-Hall-Hausman (BHHH) algorithm. Simultaneous testing of model parameters using the Maximum Likelihood Ratio Test (MLRT) and partial testing using the Wald test. The developed model is applied to modelling data on education performance indicators with response variables of Mean of Years Schooling (MYS), School Enrolment Rate (SER) for 16-18 years old, and Gross Enrolment Rate (GER) of SMA/equivalent Regency/City in Central Java during the period 2017 to 2021. Meanwhile, the predictor variables used are GRDP per capita, Percentage of Poor Population, Gender Ratio, Percentage of Households with Access to Proper Sanitation, Labour Force Participation Rate, and Student to Teacher Ratio in Junior High School. MGGR modelling results show that all predictor variables simultaneously have a significant effect on all response variables. Meanwhile, the GTWMGGR models produced different predictor variables that had a significant effect on each regency/city in Central Java. The GTWMGGR model resulted in the best accuracy because it accommodated the spatio-temporal heterogeneity effect.

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	Algoritma BHHH, Generalized Gamma, GTWMGGR, MGGR, MLE, Spatio-temporal Model.
Subjects:	H Social Sciences > HA Statistics H Social Sciences > HA Statistics > HA30.6 Spatial analysis
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User:	Hasbi Yasin
Date Deposited:	05 Feb 2025 12:11
Last Modified:	05 Feb 2025 12:14
URI:	http://repository.its.ac.id/id/eprint/118395

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