GEOGRAPHICALLY WEIGHTED QUANTILE REGRESSION MODELLING ON HUMAN DEVELOPMENT INDEX IN JAVA ISLAND

Neny Kurniawati., Henny Pramoedyo., and Suci Astutik

Abstract:

Quantile regression analysis is a regression method with an approach to dividing data into certain quintiles that may have different predictive values. Although it is not specified as a robust method, quantile regression can be applied to data that containing outliers and has a non-homogeneous variance of errors. If the variance of errors is not homogeneous, it’s likely that a globally generated model won’t be able to explain the entire data so that a locally generated model is needed by including spatial elements. Conditions that are influenced by spatial elements allow for spatial heterogeneity. GWR is a method that can be used to predict model parameters in data that have spatial heterogeneity. To accommodate two aspects at once, namely the the exploration of relation patterns between variables that are influenced by spatial heterogeneity factors and the distribution pattern of response variables, Geographically Weighted Quantile Regression (GWQR) was developed. In this study, the GWQR model was applied to Java Island’s HDI data where its achievement was very diverse and a cause for spatial problem. The weight that used in this research is the Adaptive Gaussian Kernel and the quantile value that used is 0.05; 0.25; 0.50; 0.75; and 0.95. The analysis shows that the GWQR model is better than the global QR model in explaining the relationship between life expectancy (years), school enrollment rates aged 16-18 years (%), percentage of the population with minimum high school education (%), population density (km2/soul), percentage of poor people (%), and expenditure per capita (rupiah) towards the IPM of districts/cities in Java Island. This can be seen from the results of the predictions produced by the GWQR model which is closer to the actual IPM value than the prediction results generated from QR models globally and also base on the value of RMSE. The RMSE value of GWQR model for each quantile are less than RMSE value of global QR.

 

Keywords: quantlile regression, outliers, spatial heterogeneity, Geographically Weighted Regression, IPM.

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