Computation of spatial error model with matrix exponential spatial specification approach

Abstract

In spatial regression analysis, we not only consider a location's internal factors but also consider the spatial factors that may affect the relationship. The model of spatial dependence between regions caused by unknown factors or errors is known as the Spatial Error Model (SEM). In its application to large datasets, SEM suffers from several problems in parameter estimation and computational time. One of the methods to solve this problem is to use Matrix Exponential Spatial Specification (MESS). This research aims to find another alternative to modeling data containing spatial autocorrelation errors as a substitute for SEM. MESS(0,1) is named as an alternative model to SEM. With the advantage of MESS features, the MESS(0,1) model is expected to be faster in analytics and computation compared to SEM when using Maximum Likelihood Estimation (MLE). This study aimed to evaluate the effectiveness of the MESS (0,1) model as an alternative to SEM using MLE based on simulation studies and real data analysis. Simulation studies were conducted by generating data from small samples to large samples and then estimating parameters with the MESS(0,1) and SEM models. Then we compared the performance of the two models with the time used during estimation and the root mean square error (RMSE). In addition, it is applied to real data, namely Gross Regional Domestic Product (GRDP) data. The real data used is the GRDP of the construction category on Java Island in 2021. This is in line with the massive infrastructure development as a government program. The independent variables used and considered influential on the GRDP of the construction sector are domestic investment, foreign investment, labor, and wages. Based on the simulation study results, the computation time for estimating the parameters of MESS(0,1) is faster than the SEM model. In addition, in terms of accuracy, the RMSE indicator shows MESS(0,1) is more accurate than the SEM. In addition, the MESS(0,1) and SEM models were applied to the real data. The modeling real data results show that all variables significantly positively affect GRDP in the construction category.