Spatial Outlier Detection Using GAMs and Geographical Information Systems

A spatial (local) outlier is a value that differs from its neighbors. The usual way in which these are detected is a complicated task, especially if the data refer to many locations. In this paper we propose a different approach to this problem that consists in considering outlying slopes in an interpolation map of the observations, as indicators of local outliers. To do this, we transfer geographical properties and tools to this task using a Geographical Information System (GIS) analysis. To start, we use two completely different techniques in the detection of possible spatial outliers: First, using the observations as heights in a map and, secondly, using the residuals of a robust Generalized Additive Model (GAM) fit. With this process we obtain areas of possible spatial outliers (called hotspots) reducing the set of all locations to a small and manageable set of points. Then we compute the probability of such a big slope at each of the hotspots after fitting a classical GAM to the observations. Observations with a very low probability of such slope will finally be labelled as spatial outliers.