Model Mixed Geographically Weighted Log-Logistik 3-Parameter Regression (Studi Kasus: Insidensi Kasus Kusta di Provinsi Jawa Tengah Tahun 2024)

Nuranisa, Nuranisa (2026) Model Mixed Geographically Weighted Log-Logistik 3-Parameter Regression (Studi Kasus: Insidensi Kasus Kusta di Provinsi Jawa Tengah Tahun 2024). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Model Mixed Geographically Weighted Log-Logistic 3-Parameter Regression (MGWLL3R) merupakan pengembangan dari model Log-Logistic 3-Parameter Regression (LL3R) dan Geographically Weighted Log-Logistic 3-Parameter Regression (GWLL3R). Model ini dikembangkan untuk memodelkan variabel respon yang berdistribusi tidak normal, menceng ke kanan (right-skewed), dan menunjukkan heterogenitas spasial, serta mampu mengakomodasi variabel yang berpengaruh secara global pada seluruh lokasi pengamatan maupun variabel yang berpengaruh secara lokal pada lokasi tertentu. Pada penelitian ini dibahas mengenai estimasi parameter dan statistik uji untuk model MGWLL3R. Hasil penelitian ini menunjukkan bahwa penaksiran parameter model MGWLL3R menggunakan Maximum Likelihood Estimation (MLE) menghasilkan persamaan yang tidak closed-form sehingga diselesaikan dengan iterasi numerik Berndt-Hall-Hall-Hausman (BHHH). Statistik uji untuk pengujian serentak menggunakan metode Maximum Likelihood Ratio Test (MLRT). Selanjutnya model diaplikasikan pada Insidensi Kasus Kusta di 35 Kabupaten/Kota Provinsi Jawa Tengah tahun 2024. Hasil analisis menunjukkan bahwa model MGWLL3R menggunakan kernel fixed gaussian dengan bandwidth optimum sebesar 0,377. Hasil analisis mengidentifikasi enam kelompok spasial yang berbeda dengan menghasilkan empat variabel lokal, yaitu tingkat pengangguran terbuka, persentase rumah tangga dengan akses air minum layak, laju pertumbuhan penduduk, dan rata-rata lama sekolah, serta satu variabel global, yaitu persentase rumah tangga dengan akses sanitasi layak. Kebaikan model diukur dengan AICc yang menghasilkan nilai AICc terendah sebesar 77,469 dibandingkan fungsi kernel lainnya. Selain itu, uji perbandingan model menegaskan bahwa model spasial ini secara signifikan lebih unggul dibandingkan model global LL3R dan GWLL3R.
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The Mixed Geographically Weighted Three-Parameter Log-Logistic Regression (MGWLL3R) model is an extension of the Three-Parameter Log-Logistic Regression (LL3R) and Geographically Weighted Three-Parameter Log-Logistic Regression (GWLL3R) models. The model was developed to analyze response variables with non-normal, right-skewed distributions and spatial heterogeneity while simultaneously accommodating predictor variables with global effects across all observation locations and local effects that vary by location. This study discusses parameter estimation and hypothesis testing for the MGWLL3R model. Parameter estimation was performed using Maximum Likelihood Estimation (MLE), which resulted in non-closed-form equations that were solved using the Berndt–Hall–Hall–Hausman (BHHH) iterative algorithm. Simultaneous hypothesis testing was conducted using the Maximum Likelihood Ratio Test (MLRT). The proposed model was applied to leprosy incidence data from 35 regencies/cities in Central Java Province, Indonesia, based on 2024 data. The results indicated that the MGWLL3R model with a Fixed Gaussian kernel achieved the best performance with an optimal bandwidth of 0.377. Spatial analysis identified six distinct spatial groups, consisting of four local predictors, namely the open unemployment rate, the percentage of households with access to safe drinking water, population growth rate, and mean years of schooling, and one global predictor, namely the percentage of households with access to proper sanitation. Model performance was evaluated using the corrected Akaike Information Criterion (AICc), and the MGWLL3R model produced the lowest AICc value (77,469) compared with other kernel functions. Furthermore, model comparison tests confirmed that the proposed spatial model significantly outperformed the global LL3R and GWLL3R models.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	BHHH, Insidensi Kasus Kusta, LL3R GWLL3R dan MGWLL3R ==================================================================================================================================================================================== BHHH, Incidence of Leprosy Cases, LL3R, GWLL3R and MGWLL3R
Subjects:	Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Nuranisa Nuranisa
Date Deposited:	05 Aug 2026 04:31
Last Modified:	05 Aug 2026 04:31
URI:	http://repository.its.ac.id/id/eprint/143942

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