Spatial Weight Matrix Comparison of SAR-X Model using Casetti Approach

Almeira Tsanawafa, Dianne Amor Kusuma, Budi Nurani Ruchjana

Abstract


The Spatial Autoregressive Exogenous (SAR-X) model with the Casetti approach is used to describe the influence of location and exogenous variables in the description and prediction of spatial observations, namely, people's habits and behavior towards culture in Java Island. The SAR-X model with the Casetti approach is characterized by a spatial weight matrix that describes the coordinates of the region at each location. The spatial weight matrix is determined outside the model. This study examines the spatial weight matrix determined based on rook contiguity, bishop contiguity, queen contiguity, inverse distance and inverse distance squared, and compares the application of the spatial weight matrix to the SAR-X model with the Casetti approach for the description and prediction of people's habits and behavior towards culture in Java Island. The description and prediction results obtained are measured using the Root Mean Square Error (RMSE) value. The results of data processing show that the best spatial weight matrix in the SAR-X model with the Casetti approach to community habits and behavior in Java Island is the inverse distance squared spatial weight matrix, supported by the calculation of the minimum RMSE value and the coefficient of determination above 60%.


Keywords


mathematics; spatial, stochastic

Full Text:

PDF

References


[1] A. Tsanawafa, D. A. Kusuma, and B. N. Ruchjana, “Penerapan Model Spatial Autoregressive Exogenous pada Data Penetapan Warisan Budaya Takbenda di Pulau Jawa,” Jurnal Matematika Integratif, vol. 19, no. 2, p. 137, Dec. 2023, doi: 10.24198/jmi.v19.n2.46526.137-147.

[2] D. Hidayati, “Memudarnya Nilai Kearifan Lokal Masyarakat dalam Pengelolaan Sumber Daya Air (Wang Value Of Local Wisdom in the Management of Water Resources),” 2016.

[3] A. Setiawan Abdullah et al., Model SAR, Ekspansi SAR dan Plot Moran untuk Pemetaan Hasil Akreditasi Sekolah di Provinsi Jawa Barat. 2015.

[4] H. Yasin, B. Warsito, and A. Hakim, “REGRESI SPASIAL (Aplikasi dengan R),” 2020.

[5] T. Wuryandari, A. Hoyyi, D. S. Kusumawardani, and D. Rahmawati, “Identifikasi Autokorelasi Spasial pada Jumlah Pengangguran di Jawa Tengah Menggunakan Indeks Moran,” MEDIA STATISTIKA, vol. 7, no. 1, Jun. 2014, doi: 10.14710/medstat.7.1.1-10.

[6] M. H. Mukrom, H. Yasin, and A. R. Hakim, “Pemodelan Angka Harapan Hidup Provinsi Jawa Tengah Menggunakan Robust Spatial Durbin Model,” Jurnal Gaussian, vol. 10, no. 1, pp. 44–54, 2021, doi: 10.14710/j.gauss.v10i1.30935.

[7] E. Maria, E. Budiman, Haviluddin, and M. Taruk, “Measure distance locating nearest public facilities using Haversine and Euclidean Methods,” in Journal of Physics: Conference Series, Institute of Physics Publishing, Mar. 2020. doi: 10.1088/1742-6596/1450/1/012080.

[8] Sukarna, W. Sanusi, and Hafilah. H, “Analisis Moran’s I, Geary’s C, dan Getis-Ord G pada Penerapan Jumlah Penderita Kusta di Kabupaten Gowa,” Journal of Mathematics, Computations, and Statistics, vol. 2, no. 2, pp. 151–163, 2019.

[9] H. P. A. Y. , Helmi, “Metode Maximum Likelihood dalam Penaksiran Model Spastial Autoregressive (Studi Kasus: Indeks Pembangunan Manusia Seluruh Provinsi di Indonesia pada Tahun 2016),” Bimaster : Buletin Ilmiah Matematika, Statistika dan Terapannya, vol. 8, no. 3, pp. 437–447, 2019, doi: 10.26418/bbimst.v8i3.33585.

[10] F. Indra Sanjaya and D. Heksaputra, “Prediksi Rerata Harga Beras Tingkat Grosir Indonesia dengan Long Short Term Memory,” vol. 7, no. 2, pp. 163–174, 2020, [Online]. Available: http://jurnal.mdp.ac.id

[11] I. Ghozali, Aplikasi analisis multivariate dengan program IBM SPSS 25 edisi ke-9. Universitas Diponegoro, 2018. [Online]. Available: http://slims.umn.ac.id//index.php?p=show_detail&id=19545

[12] S. Hosseini, R. Pourmirzaee, D. J. Armaghani, and M. M. Sabri Sabri, “Prediction of ground vibration due to mine blasting in a surface lead–zinc mine using machine learning ensemble techniques,” Sci Rep, vol. 13, no. 1, p. 6591, Apr. 2023, doi: 10.1038/s41598-023-33796-7.




DOI: https://doi.org/10.18860/ca.v9i1.25579

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 Almeira Tsanawafa, Dianne Amor Kusuma, Budi Nurani Ruchjana

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.