Comparing the Accuracy of the Exponential Spatial Model using a Suggested Optimization Method

Abstract

 Spatial models have been of great importance in the study of spatial relationships and economic and geographical phenomena. As a result of this importance, researchers have highlighted the development of spatial data modeling in accordance with the foundations and assumptions of those models, and their use has spread in many fields and applications.

One of the widely used spatial models is the Spatial Autoregressive (SAR) model, but one of the shortcomings of this model is that it requires the availability of its own conditions and assumptions and restrictions on its parameters to achieve stability, so the described as The Matrix Exponential Spatial Specification Model (MESS) appeared that exceeds the restrictions. imposed, which is characterized by constructing a matrix of spatial adjacencies in the form of an exponential matrix. A new method was proposed to improve prediction accuracy by using a mechanism to calculate the matrix of exponential spatial weights called (the spectral analysis method). The matrix of spatial exponential weights was also calculated based on two methods (the Taylor series method). (And the Suggested method). The model parameters were estimated using the Quasi-Maximum likelihood (QML) method. Simulations were performed for three sample sizes (35, 75, 150). A program was designed in the R programming language to calculate the exponential matrix and estimate the model parameters. The results showed When using the exponential matrix spatial according to the Suggested method, it is the best for all sample sizes and different levels of variance compared to the Taylor series method