Robust geographically weighted regression with least absolute deviation (case study: the percentage of diarrhea occurrence in semarang 2015)

Abstract

Diarrhea is one of many health issues in the developing country like Indonesia because the sickness and the death number are still high. According to the health profile of Semarang City, the people who suffer from diarrhea from 2010-2015 are decreasing. The lowest point happened in the year 2013 with the total case of 38.001. However, there is an increasing number from 2014-2015. The distribution data of diarrhea is spatial data. The differences between environment and sanitation could cause spatial heterogeneity. The spatial heterogeneity could cause the produced variant value no longer constant, but instead, it is different in each region. Therefore, the regression model that involves the effects of spatial heterogeneity is needed, which are Geographically Weighted Regression (GWR) that is built by Weighted Least Square (WLS) adjuster. Although, GWR parameter adjuster that used WLS is very sensitive with the existence of outliers. The existence of the outlier in the data will create a vast residual. Thus, a more robust method is needed, which is the Least Absolute Deviation (LAD) methods in order to estimate the parameter on model GWR. This model is called Robust GWR (RGWR). The result shows that the model events of diarrhea on each region in Semarang City are different. Furthermore, the model events of diarrhea with the RGWR model generate MAPE 16.3396% which means the performance of RGWR is formed well.