Parameter estimation of geographically weighted regression (GWR) model using weighted least square and its application

Linear regression is a method that can be used to model the relationship between a dependent variable to one or more independent variables. There are some assumptions that must be fulfilled in the linear regression model, such as the error term is normally distributed with mean zero, constant error variance (homoscedasticity), and the error between observations are independent. When analyzing spatial data using a linear regression model, sometimes the homoscedastic assumption cannot be fulfilled because data condition on one location can be different with data condition in other location. Geographically Weighted Regression (GWR) model can be used to overcome the spatial heterogeneity problem. Parameters of GWR model can be estimated using Weighted Least Squares (WLS) method as basic of estimating parameters. As the weight is kernel weighting function. Kernel weighting function used in this paper is Gaussian kernel weighting function. There is an example of the GWR model application by using inpatient claims data of PT. XYZ members to see the relationship between the total inpatient cost to the hospitalization duration and hospital's room type for Typhoid Fever. Based on the map of parameter estimation on GWR model, it can be seen that there is a variation of the total inpatient cost in every subjects location. If only the linear regression model is used to analyze this data, there will be a misleading interpretation so that it is suitable to model the data with GWR model.