»[E]verything is related to everything else, but near things are more related than distant things.« (First law of geography; Waldo Tobler, 1970)
The world around us is full of complex spatial structures. But how can we reliably estimate meaningful spatial structures from our scientific and everyday data sets? What stories do quantified spatial patterns tell us? How do spatial methods interact with different types of data and their properties? How can we approach the identification of spatial structures in novel types of data sets? These are the questions we are dealing with at the Spatial Modelling Lab Dortmund.
Our lab focuses on statistical methods for the detection and characterisation of spatial regularities. One specialisation is the estimation of spatial autocorrelation. We investigate how existing estimators interact with novel data sets for which these methods were not originally intended. An example is the case of social media data, some of which are geographically referenced. However, such Big Data sources are subject to complex forms of heterogeneity and originate from largely uncontrolled, non-scientific data collection procedures. Using existing methods or novel approaches, we investigate how we can extract spatial patterns from such data sets in order to expand our knowledge about the organisation of our everyday life. We thereby contribute to the investigation of correlation measures, hotspot statistics, and measures of spatial heterogeneity.
We also focus on new ways of representing "space" in regression and other types of modelling. This includes the explicit inclusion of space as an explanatory factor in regression models to reveal the effect of space in complex systems. Our work investigates both methodological aspects of both regression modelling and spatial filtering. The latter is a set of techniques based on the representation and understanding of the interplay of all possible spatial patterns that a specific geographic configuration would theoretically allow. This holistic approach makes spatial filtering a very powerful tool for a comprehensive quantitative analysis of geographical issues. In addition to these technical foci, we emphasise the importance of modelling not only space in an abstract sense, but especially geographical space. In this way, we argue for the importance of the meaningfulness that models of geographical space should offer in order to disclose not only patterns and structures, but also a detailed and realistic understanding of the geographical environment. This is a key feature that distinguishes us from many other, more technically oriented labs and positions us clearly at the interface between technical and domain expertise.