Influence diagnostics in geographically weighted ridge regression

Abstract

The presence of influential observations affect the accuracy of the model results. Similarly, the multicollinearity is the other problem that affect accuracy. Literature has shown that both the presence of influential observations and multicollinearity can arise in the model at the same time. This situation is also encountered in the geographically weighted regression. This study introduces the case-deletion diagnostics for the ridge estimator in geographically weighted regression model. To identify the influential observations, Cook’s Distance and Pena’s Statistics are adapted for the geographically weighted ridge regression model. The proposed diagnostics have been applied through a well-known real data. The influential observations have been detected by Cook’s Distance and Pena’s Statistics plots in real data. In addition, the simulated data has been used to reveal the performance of the proposed diagnostics. The results of the simulation showed that Pena’s Statistics has been very good at detecting high leverage outliers in the large data sets, especially.