Robust spatial Durbin modelling on tuberculosis data using the MM-estimator method

Abstract

The spatial Durbin model (SDM) is a spatial regression model which shows the existence of spatial dependency on the response variable and predictor variables. However, SDM modelling may sometimes involve problems associated with e.g. the existence of spatial outliers. One way to overcome outliers in the SDM model is to use robust regression in the form of the robust spatial Durbin model (RSDM). This study aims to estimate the parameters of RSDM based on data on tuberculosis (TB) cases recorded in 2020 in the South Sulawesi Province in Indonesia and to identify the factors that affect the number of TB cases in the region. The MM-Estimator robust regression estimation method was used. It is a combination of a method involving a high breakdown value for the S-estimator and a high efficiency of the M-estimator. The results of the analysis show that RSDM can overcome outliers in spatial regression models. This is reflected in the value of the mean square error (MSE) of the RSDM, which is 6,461.734, i.e. smaller than the value of the SDM model, and the adjusted R^2 value of 99.52%, which is greater than that of the SDM model. The factors that influence the number of TB cases in the South Sulawesi Province are population density, the percentage of households leading a healthy lifestyle, the percentage of residents with Bacillus Calmette-Guérin (BCG) immunisation, and the percentage of those suffering from malnutrition.