Spatial Regression Model with Optimum Spatial Weighting Matrix on GRDP Data of Sulawesi Island

Abstract

The two main spatial regression models are the spatial autoregressive model (SAR) and spatial error model (SEM). The extension of the SAR model is a spatial Durbin model (SDM), which considers the spatial dependence of response and explanatory variables. However, the determination of the spatial weight matrix is critical for the best estimation results. We consider two distance-based spatial weight matrices, i.e., the k-Nearest Neighbour (k-NN) and Inverse Distance Weighting (IDW). The objective of this study was to compare the performance of the Ordinary Least Squares (OLS) regression, SAR, SEM, and SDM models with k-NN and IDW on the estimation of Growth Regional Domestic Product (GRDP) and identify the critical factors that influence the value of GRDP of Sulawesi island. The study used the GRDP data of 81 districts/cities in Sulawesi island in 2018 with six explanatory variables. The results show that the 4-NN weighted SAR model outperforms the OLS, the 4-NN SEM, SDM models, IDW SAR, SEM, and SDM models. The factors that influence the value of GRDP in Sulawesi island are HDI (Human Development Index), population size, open unemployment, small/micro and medium industries, and the spatial lag autoregressive coefficient.