Presentation at AGILE 2023 in Delft
The AGILE conference is one of the major annual European conferences in the field of geographic information science. This year, RAM contributed a short paper presented by René Westerholt in the session "Geoinfo Theory". The paper discusses inferences about estimators of spatial autocorrelation in contexts where not only the attributes but also the underlying spatial units are allowed to vary. Spatial autocorrelation is a fundamental statistical property of geographic data and a number of estimators have been introduced. Moran’s I, the method discussed during the talk, is thereby one of the most commonly used methods. Most estimators of spatial autocorrelation are based on assessing the degree of correspondence between structures in an attribute and structures among spatial units, both of which are operationalised in matrix form. Associated inference procedures then rely on holding the spatial configuration fixed, but varying the attribute values over the geometries. Although fixing the geometries is useful in many scenarios, there are cases where it would be more appropriate to allow the geometries to vary as well, such as in the analysis of social media feeds or mobile sensor observations. In the presented short paper, the case is considered where geometries are the result of inhomogeneous spatial Poisson processes. Using diagonal and circular types of spatial structuring, it is investigated how random geometries affect critical values used to assess the significance of global Moran’s I scores. It is shown that the critical values resulting from an established inference framework often underestimate the bounds that would result if geometric randomness were taken into account. This leads to type-I errors and thus potential false positive patterns. In addition, the talk also briefly discussed the results of an article we published at the end of last year in the journal Geographical Analysis. In this paper, two other types of point processes, Thomas and Matérn processes, are considered. References to both the short paper and the journal article can be found below.
Westerholt, R. (2023): Studying critical values for global Moran's I under inhomogeneous Poisson point processes. 26th AGILE International Conference on Geographic Information Science (AGILE 2023), Delft, the Netherlands. DOI: 10.5194/agile-giss-4-52-2023.
Westerholt, R. (2022): A simulation study to explore inference about global Moran’s I with random spatial indexes. Geographical Analysis, volume and issue pending. DOI: 10.1111/gean.12349.