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

Almeira Tsanawafa (Master of Mathematics Study Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences Universitas Padjadjaran)
Dianne Amor Kusuma (Department of Mathematics Universitas Padjadjaran)
Budi Nurani Ruchjana (Department of Mathematics Universitas Padjadjaran)

CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 9, No 1 (2024): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

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%.