The impact of spatial outliers on spatial correlation: the role of the local influence function

Abstract In the analysis of large spatial datasets, identifying and treating spatial outliers is essential for accurately interpreting geographical phenomena. While spatial correlation measures, particularly Local Indicators of Spatial Association (LISA), are widely used to detect spatial patterns, the presence of abnormal observations may frequently distort the landscape and conceal critical spatial relationships. Traditional influence function (IF) methodologies, commonly used in statistical analysis to measure the impact of individual observations on statistical measures, are not applicable in the spatial context because in this case the influence is determined not only by the value observed in a spatial unit, but also by its location, its connections with neighboring regions, and by the values observed in neighboring observations. In this paper, we introduce a local version of the influence function (called “Local Influence Function”, or LIF for short) that accounts for spatial dependence in robustness analysis. In the paper, we first derive the analytical expression of the local influence function and we suggest a way of summarizing it in a single parameter. We then show, through the analysis of both simulated and real-world datasets, how the LIF provides a more nuanced and accurate description of the effects of spatial outliers in the analysis of spatial correlation and we discuss its interpretation in comparison with the local Moran index.