Development life expectancy model in Central Java using robust spatial regression with M-estimators

Abstract

Spatial regression model is used to determine the relationship between the dependent and independent variables with spatial influence. In case only independent variables are affected, Spatial Cross Regressive (SCR) Model is formed. Spatial Autoregressive (SAR) occurs when the dependent variables are affected, while Spatial Durbin Model (SDM) exists when both variables exhibit effects. The inaccuracy of the spatial regression model can be caused by outlier observations. Removing outliers in the analysis changes the spatial effects composition on data. However, using robust spatial regression is one way of overcoming the outliers in the model. Moreover, the typical parameter coefficients, which are robust against the outliers, are estimated using M-estimator. The research develops the life expectancy model in Central Java Province through Robust-SCR, Robust-SAR, and Robust-SDM to reduce spatial outliers' effect. The model is developed based on educational, health and economic factors. According to the results, M-estimator accommodates the outliers’ existence in the spatial regression model. This is indicated by an increase in R² value and a decrease in MSE caused by the change in the estimating coefficient parameters. In this case, Robust-SDM is the best model since it has the biggest R² value and the smallest MSE.