A goodness of fit test of geographically weighted polynomial regression models and its application on life expectancy modelling

Geographically weighted polynomial regression (GWPolR) is a spatial model with varying coefficients and polynomial relationships between response and its predictors. It is a generalisation of geographically weighted regression (GWR) models. By this generalisation, it has more parameters and better goodness of fit measures than the GWR does. Nevertheless, it is important to decide statistically whether the GWPolR model describes a given data set significantly better than a GWR model does. So, to carry out the work this paper aims to derive an ANOVA type test statistic and provide a guideline for performing the test in practice. Then, two simulated data sets were used to evaluate test performance. Those examples have shown that the test procedure has performed well and has provided a feasible way to choose an appropriate model for a given data set. In Human Development Index modelling, the GWPolR model was not significantly better than GWR model.