Detection of Influential Observations in Spatial Regression Model Based on Outliers and Bad Leverage Classification

Abstract

Influential Observations, which are outliers in x direction, y direction or both, remain a hitch in classical regression model fitting. Spatial regression model, with peculiar nature of outliers due to their local nature, is not free from the effect of such influential observations. Researchers have adapted some classical regression techniques to the spatial models and yielded satisfactory results. However, masking or/and swamping remain stumbling block to such methods. We obtained the spatial representation of the classical regression measures of diagnostic in general spatial model. Commonly used diagnostic measure in spatial diagnostic, the Cook's distance, is compared to some robust methods, Hi2 (using robust and non-robust measures), and classification based on generalized residuals and diagnostic generalized potentials, ISRs-Posi and ESRs-Posi, with the help of the obtained spatial prediction residuals and the spatial leverage term. Results of simulation and applications to real data have shown the advantage of the ISRs-Posi and ESRs-Posi due to classification of outliers over Cook's distance and non-robust Hsi12, which suffer from masking, and robust Hsi22 which suffer from swamping in general spatial model.