Fast Maximum Likelihood Estimation of Big Data Spatial Autoregressive Model: Matrix Exponential Spatial Specification Approach

In big data, Spatial Autoregressive models experience several difficulties in parameter estimation, such as non-linear optimization, theoretical complexity, and computation. One way to overcome these difficulties is by using the matrix exponential. Matrix Exponential Spatial Specification is an alternative model for an autoregressive type spatial model using an exponential matrix. Labeled MESS(1,0) is a model to replace the spatial autoregressive model. The properties possessed by MESS(1,0) cause the MESS(1,0) model to be more advantageous than the Spatial Autoregressive model when using Maximum Likelihood Estimation. In addition to being fast in estimation, the parameters of the estimation results obtained from the MESS(1,0) model are similar to the outputs of the Spatial Autoregressive model. In addition, MESS(1,0) has a smaller Root Mean Square Error than the Spatial Autoregressive model. By looking at these advantages, the MESS(1,0) model is applied to model the Gross Regional Domestic Product of a regency or city on Java Island in the manufacturing industry sector. The Gross Regional Domestic Product of the manufacturing industry sector plays an important role in economic growth in Indonesia. The predictor variables used and affecting the Gross Regional Domestic Product of the manufacturing industry sector are investment, employees, and wages. The simulation results prove that the MESS(1,0) model parameter estimation results are more efficient and more accurate than the SAR model. From the results of Gross Regional Domestic Product modeling, it is obtained that all predictor variables have a significant positive effect on Gross Regional Domestic Product using two spatial weights.