Spatially Weighted Interaction Models (SWIM)

One of the key concerns in spatial analysis and modeling is to study and analyze the processes that generate our observations of the real world. The typical global models employed to do this, however, fail to identify spatial variations in these processes because they assume that the processes being investigated are spatially stationary. In many real-life situations, spatial variations in relationships seem plausible and at least worth examining so that the assumption of global stationarity is, at best, unhelpful and, at worst, unrealistic. In contrast, local spatial models allow for potential variations in relationships over space leading to greater insights into the data-generating processes. In this study, a framework for localizing spatial interaction models, based on geographically weighted techniques, is developed. Using the framework, we construct a family of spatially weighted interaction models (SWIM) that can help in detecting, visualizing, and analyzing spatial nonstationarity in spatial interaction processes. Using custom-built algorithms, we apply both traditional interaction models and SWIM to a journey-to-work data set in Switzerland. The results of the model calibrations are explored using matrix visualizations, which suggest that SWIM provide useful information on the nature of spatially nonstationary processes leading to spatial patterns of flows.