Mahmudah, Ika Shofiatul (2025) Perbandingan Estimasi Parameter Pada Poisson Point Process on a Linear Network dengan Pendekatan Skema Berman-Turner dan Random Quadrature. Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Model point process on linear network menjadi alternatif model untuk analisis data point pattern yang terjadi di jaringan linier seperti lokasi kecelakaan di jalan raya. Untuk estimasi parameter, berbasis maximum likelihood estimation (MLE) dan metode numerical quadrature. Pada umumnya estimasi parameter yang digunakan yaitu dengan pendekatan skema Berman-Turner. Namun demikian, pendekatan tersebut kurang cocok jika diterapkan pada data berdimensi besar yang melibatkan banyak variabel penyerta atau kovariat. Skema Berman Turner memerlukan waktu komputasi yang lama, dikarenakan dilakukan generate dummy point dengan jumlah yang lebih besar daripada jumlah observasi. Pada penelitian ini mempertimbangkan pendekatan lain yaitu menggunakan Random Quadrature. Pemodelan yang melibatkan banyak kovariat, memerlukan seleksi variabel agar model lebih sederhana, salah satunya dengan metode regularisasi Lasso. Pendekatan Random Quadrature dengan regularisasi Lasso diterapkan untuk analisis persebaran lokasi kecelakaan lalu lintas di Kabupaten Nganjuk. Hasil analisis menunjukkan pendekatan Random Quadrature memiliki kinerja lebih baik daripada skema Berman-Turner berdasarkan kriteria BIC, jumlah dummy point, dan waktu komputasi. Random Quadrature menghasilkan nilai BIC sebesar 15507 yang lebih kecil dibandingkan nilai BIC skema Berman-Turner sebesar 134526. Selain itu, Random Quadrature hanya menggunakan 8041 dummy point, jauh lebih sedikit dibandingkan skema Berman-Turner yang memerlukan 23473 dummy point. Dari segi efisiensi waktu, Random Quadrature memiliki waktu komputasi 6,92 detik lebih cepat dibandingkan skema Berman-Turner yang membutuhkan waktu 10,89 detik. Kovariat yang signifikan berpengaruh terhadap kecelakaan lalu lintas adalah jarak ke lokasi lampu lalu lintas terdekat, jenis jalan, dan jumlah lalur. Informasi ini digunakan sebagai bahan pertimbangan pemerintah Kabupaten Nganjuk dalam menyusun kebijakan untuk mencegah kecelakaan lalu lintas dan sebagai peringatan dini mengenai lokasi-lokasi yang rawan terjadi kecelakaan lalu lintas.
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Point process on linear network model becomes an alternative model for analyzing point pattern data that occurs in linear networks, such as accident locations on highways. For parameter estimation, based on maximum likelihood estimation (MLE) and followed by the numerical quadrature method. Generally, the parameter estimation used is with the Berman-Turner scheme approach. However, this approach is less suitable when applied to high-dimensional data involving many covariates or accompanying variables. The Berman Turner scheme requires a long computation time because, in principle, it generates dummy points in a quantity greater than the number of observations. In this study, another approach is considered, namely using Random Quadrature. Modeling that involves many covariates requires variable selection to simplify the model, which can be done using the Lasso regularization method. The Random Quadrature approach with Lasso regularization is applied to analyze the distribution of traffic accident locations in Nganjuk Regency. The analysis results show that the Random Quadrature approach performs better than the Berman-Turner scheme based on the BIC criteria, the number of dummy points, and the computation time. Random Quadrature produces a BIC value of 15507, which is smaller than the BIC value of the Berman-Turner scheme, which is 134526. Additionally, Random Quadrature only uses 8041 dummy points, much fewer compared to the Berman-Turner scheme which requires 23473 dummy points. In terms of time efficiency, Random Quadrature has a computation time that is 6.92 seconds faster compared to the Berman-Turner scheme, which takes 10.89 seconds. The parameter estimation results using the Random Quadrature approach revealed significant covariates, namely the distance to the nearest traffic light location, road type, and number of lanes. This information can be used as a consideration for the Nganjuk Regency government in formulating policies to prevent traffic accidents and provide information about locations prone to traffic accidents.
Item Type: | Thesis (Masters) |
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Uncontrolled Keywords: | Berman-Turner, Kecelakaan Lalu Lintas, Linear Network, MLE, Random Quadrature, Regularisasi, Spatial Point Process |
Subjects: | H Social Sciences > HA Statistics > HA30.6 Spatial analysis |
Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis |
Depositing User: | Ika Shofiatul Mahmudah |
Date Deposited: | 03 Feb 2025 01:49 |
Last Modified: | 03 Feb 2025 01:49 |
URI: | http://repository.its.ac.id/id/eprint/117733 |
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